Another algebra problem: 13=12x-2y?

Question

The question is rewrite the equation so that "y" is a function of "x". Please show work (step by step).

Here is an example: 2x+y=5 you subtract 2x by itself and the 5. Which leads to y=5-2x. Thats the answer to that example.

I dont get this problems today! I really need help!

Answer 1

math.columbia.edu/~niccolai/.../resources/Sum04midtermsolutions.pdf

http://www.e-news2.com/group-277-101.html

Commentary


Section 2-5: The Distributive Property (pp. 65-69)
Let's examine the problem 5(3 + 4). Using the agreed upon order of operations, you add the 3 and 4, then multiply the sum by 5.

5(3 + 4) ==> 5(7) ==> 35
Another method uses the distributive property and distributes the 5 throughout the quantity. This requires multiplying everything inside the parentheses by the 5.

5(3 + 4) ==> 5(3) + 5(4) ==> 15 + 20 ==> 35
Fantastic! The result is still 35. Would it work if the quantity involved subtraction?


6(8 – 4) ==> 6(4) ==> 24 and 6(8 – 4) ==> 6(8) – 6(4) ==> 48 – 24 ==> 24
Yes, it works. The use of the distributive property is a must when variables are involved.

In the problem 4(3 + 5x), you cannot find the sum because you do not know the value of 5x. But using the distributive property allows you to simplify the expression.


4(3 + 5x) ==> 4(3) + 4(5x) ==> 12 + 20x
Again, you cannot add the 12 and 20x because the value of 20x is not known. More examples follow:


5(8 + 2x – 2) + 6x Use the distributive property.
5(8) + 5(2x) – 5(2) + 6x
40 + 10x – 10 + 6x Use the commutative property.
40 – 10 + 10x + 6x Add like terms. The 10x and 6x can be added because they are both multiplied by x.
30 + 16x

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6(a + 2x) – 2a + 2x ==> 6(a) + 6(2x) – 2a + 2x ==> 6a + 12x – 2a + 2x
6a – 2a + 12x + 2x ==> 4a + 14x Terms with a and terms with x can be added. These are referred to as like terms.

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Seven more than the sum of –4 and 6y increased by one-half of the difference between 4y and 16.

7 + (–4 + 6y) + ½(4y – 16) ==> 7 + –4 + 6y + ½(4y) – ½(16)
7 – 4 + 6y + 2y – 8 ==> 7 – 4 – 8 + 6y + 2y ==> –5 + 8y

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4[3y + 5(x + 2) + (6 – y)] Start inside the brackets.
4[3y + 5(x) + 5(2) + 6 – y] ==> 4[3y + 5x + 10 + 6 – y]
4[3y – y + 5x + 10 + 6] ==> 4[2y + 5x + 16] Use the distributive property.
4(2y) + 4(5x) + 4(16) ==> 8y + 20x + 64


Study Exercises
Complete the odd-numbered problems 1-77 in the Written Exercises on pages 67-69 of your text. You could review previous material by working through the Mixed Review on page 69. Check your answers as you go against those in the back of the text.
Section 2-6: Rules for Multiplication (pp. 70-74)
This section introduces you to multiplication involving negative numbers. The rules for multiplying negative and positive numbers follow:

If the signs of the two numbers are the same, the product is positive.

If the signs of the two numbers are different, the product is negative. For example:

–6 · 4 = –24 The signs are different.
–3 · –4 = 12 The signs are the same.
5 · –3 = –15 The signs are different.
3 · 8 = 24 The signs are the same.


If a problem has more than two numbers multiplied together, you can count the negative signs. If there is an even number of negative signs, the product will be positive. If there is an odd number of negative signs, the product will be negative. For example:

(–8)(–4)(–2)(1)(–1)= 64 Four negative signs, an even number, positive result.
(–2)(–1)(–1)(–3)(7)(–1) = –42 Five negative signs, an odd number, negative result.

Throughout the remainder of your algebra career, expressions such as 5x – 7 will not be rewritten as 5x + (–7). You can determine the sign of a term by the addition or subtraction sign preceding it. In the expression –2x2 + 3x – 4y, there are two negative terms (which are underlined) and one positive term (which is bold). Keep this in mind as you are multiplying positive and negative numbers in this section.


(–1)(–z + y – 8) Use the distributive property.
(–1)(–z) + (–1)(y) + (–1)(–8) Keep the negative sign with the 8; always place plus signs between the products.
z – y + 8 Use rules of multiplication: (–1)(–z) same signs, positive result; (–1)(y) different signs, negative result; (–1)(–8) same signs, positive result.

--------------------------------------------------------------------------------

(–2)(–3 – x + 4y) The 3 is negative, x is negative, and 4y is positive.
(–2)(–3) + (–2)(–x) + (–2)(4y) Distribute the –2 throughout the quantity.
6 + 2x – 8y

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–3(2x + y) – 6(x – 3y) The 6 is negative. Keep the sign with the 6 when distributing it throughout the quantity.
(–3)(2x) + (–3)(y) + (–6)(x) + (–6)(–3y)
–6x – 3y – 6x + 18y Add like terms. Add x and y terms together.
–12x + 15y Remember, you cannot add x terms to y terms.

A note about the second line of the above problem: Always keep the negative sign with the term and place a plus sign between the terms. The 6 is negative because of the minus sign in front of it. I kept the sign with the 6 and placed plus signs before the (–6)'s.

--------------------------------------------------------------------------------

–8 – 3[3(x – 5) – 4(1 – x)] Start within the brackets.
–8 – 3[(3)(x) + (3)(–5) + (–4)(1) + (–4)(–x)] Distribute 3 and –4 throughout the quantities.
–8 – 3[3x – 15 – 4 + 4x] Multiply.
–8 – 3[7x – 19] Add x terms and constants.
–8 + (–3)(7x) + (–3)(–19) Distribute –3 throughout the quantity.
–8 – 21x + 57 ==> 49 – 21x or –21x + 49

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Study Exercises
Complete the odd-numbered problems 1-55 in the Written Exercises on pages 72-73 of your text. For extra practice, try the Mixed Review on page 73. Then check your answers in the back of the text.

Section 2-7: Problem Solving: Consecutive Integers (pp. 75-78)
This section provides practice in using parentheses as grouping symbols in writing equations. Consecutive integers, consecutive even integers, and consecutive odd integers are the basis of the equations. Remember, integers are the set of positive and negative numbers not including fractions.
Consecutive integers are numbers that follow each other. The integers can be positive or negative unless the problem specifies a sign. Some examples follow:


five consecutive integers: 6, 7, 8, 9, 10
four consecutive integers: –8, –7, –6, –5

three even consecutive integers: 12, 14, 16

four odd consecutive integers: –47, –45, –43, –41

Let's start with a problem: Find three consecutive integers whose sum is –33. Possible values of the smallest integer are {–12, –10, 6}.

When trying to write an equation for a word problem involving consecutive integers, you should begin by listing how many numbers are involved. The above problem has " three consecutive integers."


1st number:
2nd number:

3rd number:

If the problem is not specific about what the variable should represent, give the variable to the first number. The above problem suggests the "value of the smallest integer." Remember, consecutive integers follow each other, such as 9, 10, 11. So if you know the first number you add 1 to it to get the second number. To get the third number, you add 2 to the first number. Write down a couple of lists of consecutive numbers and determine if this pattern holds true.


1st number: x
2nd number: x + 1

3rd number: x + 2

The problem states "whose sum is –33." So, x + (x + 1) + (x + 2) = –33 is the equation. Try the first element of the suggested list for x:


(–12) + (–12 + 1) + (–12 + 2) ==> –12 + –11 + –10 ==> –33
The value of x is –12. The first of the three numbers is x. The problem states "Find three consecutive integers." All three numbers need to be found.


x + 1 ==> –12 + 1 ==> –11
x + 2 ==> –12 + 2 ==> –10

The numbers are –12, –11, and –10.



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Even numbers such as 6, 8, 10, and 12 skip over the odd numbers. To jump from 6 to 8, you add 2. To jump from 6 to 10, you add 4, and so on. Odd numbers follow the same idea. The odd numbers 103, 105, and 107 skip over the even numbers. To jump from 103 to 105, you add 2. To jump from 105 to 107, you add 4, and so on.

Another problem follows: Find two consecutive even integers whose product is 120. Possible values of the smaller number are {6, 10, 12}.


1st number = x
2nd number = x + 2

x(x + 2) = 120 "whose product is 120"

Try the suggested values for x:


6(6 + 2) ==> 6(8) ==> 48
10(10 + 2) ==> 10(12) ==> 120

The value of x is 10. The first of the two numbers is x. The problem states "Find two consecutive even integers." Both numbers need to be found.

x + 2 ==> 10 + 2 ==> 12
The numbers are 10 and 12.



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Find three consecutive odd integers such that twice the smaller is 1 less than the largest. Possible values of the largest number are {3, 5, 7}.


1st number = x – 4
2nd number = x – 2
3rd number = x Since suggested answers are for the largest number, the largest number should have the variable.


twice the smaller is 1 less than the largest
2(x – 4) = x – 1

Try the suggested values for x:


2(3 – 4) = 3 – 1 ==> 2(–1) = 2 ==> –2 = 2 Not true.
2(5 – 4) = 5 – 1 ==> 2(1) = 4 ==> 2 = 4 Not true.

2(7 – 4) = 7 – 1 ==> 2(3) = 6 ==> 6 = 6 True!

The value of x is 7. The largest of the three numbers is x. The problem states "Find three consecutive odd integers." All three numbers need to be found.


x – 2 ==> 7 – 2 ==> 5
x – 4 ==> 7 – 4 ==> 3

The numbers are 7, 5, and 3.



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Find two consecutive integers such that their product is 6 more than 6 times their sum. The domain for the largest number is {9, 13, 18}.


1st number = x – 1
2nd number = x

Their product is 6 more than 6 times their sum.

x(x – 1) = 6 + 6 (x + x – 1)

Try the suggested values for x:


9(9 – 1) = 6 + 6 (9 + 9 – 1) ==> 9(8) = 6 + 6(17) ==> 72 = 108 Not true.
13(13 – 1) = 6 + 6 (13 + 13 – 1) ==> 13(12) = 6 + 6(25) ==> 156 = 156 True!

The value of x is 13. The larger of the two numbers is x. The problem states "Find two consecutive integers." Both numbers need to be found.


x – 1 ==> 13 – 1 ==> 12
The numbers are 13 and 12.


Study Exercises
Complete the odd-numbered problems 1-15 in the Written Exercises on page 77 of your text. Then check your answers in the back of the text.

Section 2-8: The Reciprocal of a Real Number (pp. 79-82)
This section requires the use of reciprocals to simplify algebraic expressions. The reciprocal of 3/4 is 4/3. When reciprocals are multiplied together the product is 1.


It holds for negative numbers too. The reciprocal of a negative number is a negative number. When two negative numbers are multiplied together, the product is a positive one. The reciprocal of 1 is 1, the reciprocal of –1 is –1, and zero has no reciprocal. No number can be multiplied by zero and obtain a product of one, because zero times any number is zero. Some examples follow:

112(1/4)(–1/7) ==> (28)(–1/7) ==> –4

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1/m(42mn) ==> · Cancel the m's ==> 42n

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–1/7(42m – 14) – (1/6)(54m + 12)
(–1/7)(42m) + (–1/7)(–14) + (–1/6)(54m) + (–1/6)(12)
–6m + 2 – 9m – 2 ==> –15m


Study Exercises
Complete the odd-numbered problems 1-33 in the Written Exercises on page 81 of your text. Also try the Mixed Review on page 82. Then check your answers in the back of the text.

Section 2-9: Dividing Real Numbers (pp. 83-86)
The rules for dividing real numbers are the same as the rules for multiplying real numbers. When two negative or two positive numbers are divided, the quotient is positive. When just one of the numbers in the division problem is negative, the quotient is negative. For example:

–30 / –5 = 6
125a / 25 = 5a

==> –14 / (–7/5) ==> · ==> 10

Another example:

Average –4, 3, 6, –9. The sum of the numbers is –4. Divide the sum by 4 since there are four numbers. The average is –1.


Study Exercises
Complete the odd-numbered problems 1-33 in the Written Exercises on page 85 of your text. Then check your answers in the back of the text.

Chapter Summary and Application
Review assignments follow. Work as many as needed to feel confident for the progress evaluation. Answers to all problems except those in the Self-Tests are in the optional Solutions Manual. Answers to some problems also appear in the back of the textbook, as noted below.

Self-Test 3, page 86, problems 1-8. Answers are in the back of the text.

www.westmarkschool.org/teachers/Cohen.html
)evaluate the expressionif a=9 and b=5
6a+2b

2)4*(5+2)*6

3)add
5/15+10/20

4)true or false
3*(6+2)=3*(2+8)

5)1 3/9+2 2/6=

6)-4-(-10)-1=

7)r=c-8s/5d for c

8)a=8rs-3k for r

9)graph
x>8

10)graph
x<=3

11)graph
x>5

12)solve the inequality
5-3x>14

13)solve for x
|x-1|=4

14)true or false
-5<5

15)find the intercepts of the line
2x-3y=6

16)what does the graph look like for
2x+2y<=6
3x-y>=3

17)what does the graph look like for
y>-3
x<2

18) 2 3/18+ 3 2/9=

19)evaluate
|6-9to the 2nd power|

20) on tuesday the tempature high was -9F. that night the temp dropped
another 12 degree. during the day the temp rose 14 degrees to reach
the high what was it?

21)If the selling price of the house, x, less the sales commission of
4% must be at least 90,000, the .96x>= 90,000
true or false?

22)solve
10x+[6x-(6x+3)]=-9(x-8)

23)solve for x
2y-2(x+3)=y-x

24)p=10rt-tk/17g for g

25)carrie is pratcing for her SAT's. her first two pratice scores are
1250 and 1380. if she wants her average score to be between 1300 and
1400 what must the range of her third score be?

26)solve
14x-6=13x

27)solve for x
12(x-12)-9x=-36+3(x-36)

28) A taxi charges 4.00 for the first mile and 2.00 for each
additional mile. wirte an inequality representing the number of miles
a passenger could travel if they could not spend more then 10.00.

29)solve the inequality
|2x+3|<=2

30)the rice town library carries 27 diffrent magazines. let L
represent the number at the lakesville library and B represent those
at the brownsville library. Write an inequality showing the
relationship between the three libraries if brownsville carries more
then 6 times the number of magazines handled by both of the other
libaries combined.

31)find the slop and y intercept
2x+2y=3

32)find the slope
(-9,-6) and (-8,-9)

33)graph the point and slope
(2,1), m=1/2

34)what is the slope intercept?
(6,24) and (10,20)

35)The graph of y=x:
a)the x axis
b)splits quadrents 1 and 3
c)is the y axis
d)splits quadrents 2 and 4

36)give the equasion of the line through (-2,6) with the slope of -3/4

37)solution set
y=9-2x and 2x-5y=15

38)solution set
3x+2y=3 and 63x-36y=11

39)solve by substitution
x+y=2
x=4y+5

40)solve by addition
x+y=-3
x-2y=-5
1)evaluate the expression if a = 9 and b = 5
6a+2b


6*a + 2*b = 6*9 + 2*5 =
= 54 + 10 =
= 64

----------------------------------------------------------

2) 4*(5+2)*6 = 4*(7)*6 =
= 28*6 =
= 168

-----------------------------------------------------------

3)add
5/15+10/20

15 = 3*5
20 = 2*2*5
Least Common Denominator (LCD) = 2*2*3*5 = 60

60/15 = 4, then:
5/15 = (5*4)/60 = 20/60

60/20 = 3, then:
10/20 = (10*3)/60 = 30/60

5/15 + 10/20 = 20/60 + 30/60 = (20+30)/60 = 50/60,
simplifying:
5/15 + 10/20 = 5/6

See for reference:
"Adding Fractions with the same Denominator"
http://www.aaamath.com/B/fra57ax2.htm

"Adding Fractions with Different Denominators"
http://www.aaamath.com/fra66k-addfracud.html

---------------------------------------------------------

4)true or false
3*(6+2)=3*(2+8)

FALSE:
3*(6+2) = 3 *(8) = 24
3*(2+8) = 3*(10) = 30

---------------------------------------------------------

5)1 3/9 + 2 2/6 =

1 3/9 = 1 + 3/9 = 9/9 + 3/9 = 12/9 = 4/3

2 2/6 = 2 + 2/6 = 12/6 + 2/6 = 14/6 = 7/3

1 3/9 + 2 2/6 = 4/3 + 7/3 = (4 + 7)/3 = 11/3

-----------------------------------------------------------

6)
-4 -(-10) - 1 = -4 + 10 -1 =
= 10 - 4 - 1 =
= 10 - (4+1) =
= 10 - 5 =
= 5

------------------------------------------------------------

7)r = c - 8s/5d for c

r = c - (8*s/5*d)

==> r + (8*s/5*d) = c - (8*s/5*d) + (8*s/5*d) =
= c

Then:
c = r + (8*s/5*d)

----------------------------------------------------------

8)a = 8*r*s - 3*k for r;

a = (8*r*s) - (3*k)

==> a + (3*k) = (8*r*s) - (3*k) + (3*k) =
= 8*r*s

==> [a + (3*k)] / 8*s = 8*r*s / 8*s =
= r

Then r = [a + (3*k)] / 8*s

----------------------------------------------------------

9)graph x>8

If this line represents the Real numbers:

<-------------------------I-------I-------------------->
-oo 0 8 +oo

The set of numbers x that x > 8 is represented by this line:

I (-------------------->
-oo 0 8 +oo


For additional reference see:
"Solving Inequalities":
http://www.purplemath.com/modules/ineqsolv.htm

-------------------------------------------------------------

10)graph x <= 3

If this line represents the Real numbers:

<-------------------------I--I------------------------->
-oo 0 3 +oo

The set of numbers x that x <= 3 is represented by this line:

<----------------------------]
-oo 3 +oo


------------------------------------------------------------

11)graph x>5

If this line represents the Real numbers:

<-------------------------I----I----------------------->
-oo 0 5 +oo

The set of numbers x that x > 5 is represented by this line:

(----------------------->
-oo 0 5 +oo


-------------------------------------------------------------

12)solve the inequality:

5 - 3*x > 14 ==> - 3*x > 14 - 5 = 9 ==>

==> (-3)*x > 9 ==> x < 9/(-3) = -3 ==>

==> x < -3

-------------------------------------------------------------

13)solve for x

|x-1| = 4 ==> (x-1) = 4 or (x-1) = -4

Case 1:
x-1 = 4 ==> x = 4+1 = 5

Case 2:
x-1 = -4 ==> x = -4+1 = -3

Solution:
x=5 or x=-3

----------------------------------------------------------

14)true or false
-5<5

TRUE:
-5<5 <==> 0 < 5 + 5 = 10

---------------------------------------------------------

15)find the intercepts of the line
2*x - 3*y = 6

Recall the intercepts of a graph are where it crosses the x- and y-axes.
See for reference "x- and y-Intercepts":
http://www.purplemath.com/modules/intrcept.htm

x-intercept (y = 0):

2*x - 3*0 = 6
Then:
2*x = 6 ==> x = 6/2 = 3
==> x=3
Then the x-intercept is the point (x,y) = (3,0)


y-intercept (x = 0)

2*0 - 3*y = 6
Then:
3*y = 6 ==> y = 6/3 = 2
==> y=2
Then the y-intercept is the point (x,y) = (0,2)

----------------------------------------------------------

16)what does the graph looks like for
2x+2y<=6
3x-y>=3

This is a system of linear inequalities, we must solve each inequality
separately and graph wich half plane each one defines, then we must
find the overlaped area.

2*x + 2*y =< 6
Since 2*x + 2*y = 2*(x+y), then
2*(x+y) =< 6 , then
x+y =< 6 , then
y =< -x + 6
That means the graph #1 is all the area below the straigh line y = -x
+ 6 , including such line.


3*x - y >= 3 , then
3*x - 3 >= y or y =< 3x - 3
That means the graph #2 is all the area below the straigh line y = 3x
- 3 , including such line.

For additional reference and some samples to see how this solutions
looks like visit the following pages:
"Graphing Linear Inequalities":
http://www.purplemath.com/modules/ineqgrph.htm

"Systems of Linear Inequalities":
http://www.purplemath.com/modules/syslneq.htm

---------------------------------------------------------

17)what does the graph look like for
y>-3
x<2

Use the method described in the previous problem to solve this easier
problem (the graph looks like an "infinite rectangle" defined by the
straight lines y=-3 and x=2, more exactly these lines divides the
plane in four parts (quadrants) -each line is parallel to one main
axis- and the "infinite rectangle" is the upper left part or quadrant
defined by these lines).

Feel free to request for a clarification if the answer to this problem
does not satisfy you.

-----------------------------------------------------------

18) 2 3/18 + 3 2/9 =

2 3/18 = 2 + 3/18 =
= 36/18 + 3/18 =
= 39/18 = 13/6

3 2/9 = 3 + 2/9 =
= 27/9 + 2/9 =
= 29/9

6 = 2*3
9 = 3*3
Least Common Denominator (LCD) = 2*3*3 = 18

Then:
2 3/18 + 3 2/9 = 13/6 + 29/9 =
= (39 + 58)/18 =
= 97/18

----------------------------------------------------------

19)evaluate
|6-9 to the 2nd power| = |6 - 9^2| =
= |6 - 9*9| =
= |6 - 81| =
= |-75| =
= 75

----------------------------------------------------------

20) on tuesday the tempature high was -9F. that night the temp dropped
another 12 degree. during the day the temp rose 14 degrees to reach
the high what was it?

Initial temp T0 = -9ºF
Then dropped 12ºF, so T1 = -9ºF - 12ºF = -21ºF;
During the day temp rose 14ºF to reach the high
T2 = -21ºF + 14ºF = -7ºF
Friday high temperature was -7ºF.

----------------------------------------------------------

21)If the selling price of the house, x, less the sales commission of
4% must be at least 90,000, the .96x>= 90,000
true or false?

If x is the selling price, then the 4% sales commission is:
0.04*x .
Then Selling price less sales commission is:
x - 0.04*x = 0.96*x
According to the problem statement this value is at least 90,000, so:
0.96*x >= 90,000 , so the statement is TRUE.

-----------------------------------------------------------

22)solve 10x+[6x-(6x+3)] = -9(x-8)


10*x + [6*x -(6*x+3)] = -9*(x-8)
Then:
10*x + [6*x - 6*x - 3] = -9*x + 72
Then:
10*x + [- 3] = -9*x + 72
Then:
10*x - 3 = -9*x + 72
Then:
10*x + 9*x = 72 +3
Then:
(10+9)*x = 19*x = 75
Then:
x = 75/19

---------------------------------------------------------

23)solve for x
2y-2(x+3)=y-x :

2*y - 2*(x+3) = y - x
Then:
2*y - (2*x + 2*3) = y - x
Then:
2*y - (2*x +6) = y -x
Then:
2*y - 2*x - 6 = y - x
Then:
2*y - 2*x - 6 + 2*x - y = y - x + 2*x - y
Then:
2*y - y - 6 = -x + 2*x
Then:
y - 6 = x

Answer:
x = y - 6

----------------------------------------------------------

24)p=10rt-tk/17g for g

p = 10*r*t - t*k/17*g
Then:
p - 10*r*t = 10*r*t - t*k/17*g - 10*r*t
Then:
p - 10*r*t = - t*k/17*g
Then:
(p - 10*r*t)*g = -(t*k/17*g)*g
Then:
(p - 10*r*t)*g = -(t*k/17)
Then:
(p - 10*r*t)*g/(p - 10*r*t) = -(t*k/17)/(p - 10*r*t)
Then:
g = -(t*k/17)/(p - 10*r*t)

-----------------------------------------------------------

25)carrie is pratcing for her SAT's. her first two pratice scores are
1250 and 1380. if she wants her average score to be between 1300 and
1400 what must the range of her third score be?

The average score of the 3 practices is:
(1250 + 1380 + x)/3 where x is the third score.
And we want that it be between 1300 and 1400, so we want:
1300 < (1250 + 1380 + x)/3 < 1400

We need to find x, we have:
1300 < (1250 + 1380 + x)/3 < 1400
Then:
1300 < (2630 + x)/3 < 1400
Then:
1300*3 = 3900 < 2630 + x < 1400*3 = 4200
Then:
3900 - 2630 < x < 4200 - 2630
Then:
1270 < x < 1570

----------------------------------------------------------

26)solve 14x-6=13x

14*x - 6 = 13*x
Then:
14*x - 6 - 13*x = 13*x -13*x = 0
Then:
(14*x - 13*x) - 6 = 0
Then:
x - 6 = 0
Then
x = 6 .

----------------------------------------------------------

27)solve for x 12(x-12)-9x=-36+3(x-36)

12*(x-12)- 9*x = -36 + 3*(x-36)
Then:
12*x - 144 - 9*x = -36 + 3*x - 3*36
Then:
(12-9)*x -144 = 3*x - 144
3*x - 144 = 3*x - 144

We have the same expression at each side of the equation, that means
the solution is valid for any value of x.

-----------------------------------------------------------

28) A taxi charges 4.00 for the first mile and 2.00 for each
additional mile. wirte an inequality representing the number of miles
a passenger could travel if they could not spend more then 10.00.

First mile charge (fixed value): 4
From mile two to x: 2 per mile = 2*(x-1)
Total charge: y = 4 + 2*(x-1)
You want that the total charge does not be more than 10 or, in other
words, to be less or equal than 10; in symbols you want total charge y
to be:
y =< 10 , then the answer is:
4 + 2*(x-1) =< 10

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29)solve the inequality
|2x+3|<=2

|2x+3| =< 2 is thae same of:
-2 =< 2x+3 =< 2
then:
-2 - 3 =< 2x =< 2-3
then:
-5 =< 2x =< -1
then:
-5/2 =< x =< -1/2

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30)the rice town library carries 27 diffrent magazines. let L
represent the number at the lakesville library and B represent those
at the brownsville library. Write an inequality showing the
relationship between the three libraries if brownsville carries more
than 6 times the number of magazines handled by both of the other
libaries combined.

Let R represent the number at the rice town library, then:
R = 27

According to the statement:
B > 6*(R+L) = 6*(27+L) = 162 + 6*L
Then:
B > 6*(R+L)
or (because we know that R = 27)
B > 162 + 6*L

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31)find the slope and y-intercept
2x+2y = 3

To solve this problem we must know that if the linear equation is:
ax + by = c , with b different to zero,
then the slope is -(a/b) and the y-intercept is the point (0,c/b).

In this case a = b = 2 and c = 3.

Then the y-intercept is the point (x,y) = (0,3/2) ;
and the slop is -(2/2) = -1.

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32)find the slope
(-9,-6) and (-8,-9)

Given two points of a line we know that:

Slope of line = Changes Vertical/Changes Horizontal
Then:
Slope of line = [-6 - (-9)] / [-9 - (-8)]
= [-6 + 9] / [-9 + 8]
= (+3)/(-1)
= -3

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33)graph the point and slope
(2,1), m=1/2

What you need here is to find the point (2,1) in the coordinate plane,
to do that just remember that the first value of the pair is the
x-value and the second is the y-value.
From this point and using the slope value, you must find a different
point of the line to graph it.
Remember the previous problem:
m = Slope = Changes Vertical/Changes Horizontal = 1/2 ;

Yes, as you are guessing the value m = 1/2 means that for each change
of 1 in the vertical direction there is a change of 2 in the
horizontal direction, so another point is easy to find by "moving"
from the point (2,1) one unit in the positive vertical direction and
two units in the positive horizontal direction, that is from (2,1) to
(2+2,1+1) = (4,2).
Now we have two points, then a straight line can by draw.

Other way is using the "slope-intercept" equation form:
We have the point (2,1), and we know that the linear equation is:
y = mx + b .
We know m and we know a pair of values for x and y that satisfies the equation:
x = 2 and y = 1 ; then we have:
1 = 1/2 * 2 + b , solving for b we have:
b = 0

So y = (1/2)*x + 0

To find another point to draw the line just give a value to x
different to the known point and use it to find the respective value
for y.
For example using 4 for x you will find y = 2, so you have found the
point (4,2) on the line, using it together with the one given in the
statement you can graph the line.


See for reference:
"Slope of a Straight Line":
http://www.purplemath.com/modules/slope.htm

"Slope-Intercept Form":
http://www.purplemath.com/modules/strtlneq.htm

"Straight-Line Equations":
http://www.purplemath.com/modules/strtlneq2.htm

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34)what is the slope intercept?
(6,24) and (10,20)

m = Changes Vertical/Changes Horizontal =
= (24-20)/(6-10) =
= 4/(-4) =
= -1

y = mx + b = -x + b

Using one of the points as data:
20 = -10 + b , solving for b:
b = 30

then y = -x + 30 is the slope intercept form of this linear equation.

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35)The graph of y=x:

a)the x axis
b)splits quadrents 1 and 3
c)is the y axis
d)splits quadrents 2 and 4

Here I guess that you need to know wich of the statements is correct.
The correct statement is b).

In the first and third quadrents x and y have the same sign, that does
not happen in the second and fourth quadrents, so in these last
quadrents the equation x=y cannot be satisfied.

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36)give the equation of the line through (-2,6) with the slope of -3/4

m = -3/4 and the pair x=-2 and y=6 satisfy the equation, then:

y = mx + b = -3/4 x + b

For x=-2 and y=6 we have:
6 = -3/4 * (-2) + b =
= 3/2 + b

Solving for b:
b = 6 - 3/2 = 12/2 - 3/2 = (12-3)/2 = 9/2

Then the equation of the line through (-2,6) with the slope of -3/4 is:
y = -3/4 x + 9/2

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37)solution set
y=9-2x and 2x-5y=15

2x-5y = 15 , since by the other equation we have that y = 9-2x , then:
15 = 2x-5y = 2x-5(9-2x) = 2x - 45 + 10x =
= 12x -45
Then:
12x = 15 + 45 = 60
Then x = 5

we had:
y = 9 - 2x = 9 - 2*5 = 9 - 10 = -1

Solution:
x = 5
y = -1

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38)solution set
3x+2y=3 and 63x-36y=11

63x-36y = 11
3x+2y = 3

From the second equation we have, solving for x:
3x + 2y = 3
Then:
3x = 3 - 2y
Then
x = (3 - 2y)/3 =
= 1 - 2/3 y

Replacing in the first equation:
11 = 63x - 36y = 63*(1 - 2/3 y) - 36y =
= 63 - 42y -36y =
= 63 - 78y

Now, solving for y:
11 = 63 - 78y
Then:
78y = 63 - 11 = 52
Then:
y = 52/78 = 26/39
then:
x = 1 - 2/3 y =
= 1 - 2/3 * 26/39 =
= 1 - 52/117 =
= 117/117 - 52/117 =
= 65/117

Solution:
x = 65/117
y = 26/39

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39)solve by substitution
x+y=2
x=4y+5

By the second equation we have:
x = 4y + 5

Replacing in the first equation:
2 = x + y = (4y + 5) + y =
= 5y + 5

Solving this for y:
5y + 5 = 2
then:
5y = 2-5 = -3
Then:
y = -3/5

Then:
x = 4y + 5
= 4 (-3/5) + 5 =
= -12/5 + 5 =
= -12/5 + 25/5 =
= (-12+25)/5 =
= 13/5

Solution:
x = 13/5
y = -3/5

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40)solve by addition

x+y=-3
x-2y=-5

Rewrite the first equation with the similar (multiplying it by 2):
2x + 2y = -6

Now we can add the second equation to the first:
2x + 2y = -6
+
x - 2y = -5
----------------
3x = -11

then x = -11/3

Replacing in the second equation:
x - 2y = -5
Then:
-11/3 - 2y = -5
then:
-2y = -5 + 11/3 = -15/3 + 11/3 = -4/3
then:
y = (-4/3)/(-2) = 2/3


Solution:
x = -11/3
y = 2/3


Additional reference for System of Linear Equations can be found at these pages:
"SYSTEMS OF EQUATIONS in TWO VARIABLES":
http://www.sosmath.com/soe/SE2001/SE2001.html

"Solving Systems of Linear Equations":
http://www.math.csusb.edu/math110/src/systems/solving.html

"Linear Algebra - System of Equations":
http://library.thinkquest.org/10030/10lsoeq.htm?tqskip1=1

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I hope this helps you. If you find something unclear or incomplete,
please request for an answer clarification before rate this answer,
due the extent of this question some typos or other little mistakes
(like misunderstanding of one problem)could happened. Also feel free
to request for further assistance is needed on graphs questions,
because is to difficult, and will give more confusion to try to draw
the graphs here. I would appreciate it if you give me a chance to
respond your requests before rate this answer if it is necessary.

Answer 2

I'm not completely sure if this is right but here.
13=12x-2y
+2y +2y
13+2y = 12x
-13 -13
2y = 12x-13
/2 /2 /2 (here you have to divide12x and 13 by 2)
y=6x-6.5 (this is your answer, i tried this problem a few different times but this was the only logical answer)

Answer 3

Oo we're doing this in math! It would be something like put 12x on the other side but make it a negative to it would be -12x +13 = 2y and then divided it all by 2 and you'll have your answer

Answer 4

i think this is how it goes cuz u wanna get the Y alone so then u do 13=12x-2y and then u subtract the 12x. making the equation -12x+13=2y divide 2
6x+13=y
y=6x+13/2

Answer 5

ok get the -2y by it self by subtracting 12 from 13
so you get 13-12x=-2y

divide -2 so you will get the y by itself and you get
y=13-12x / -2 ? i think

Answer 6

13 = 12x - 2y

subtract 12x on both sides

13-12x = -2y

divide by -2 on both sides

(13-12x)/-2 = y

move the neg. to the top

-(13 -12x)/2 =y

which is equal to

6x -(13/2) = y

Y(x) = 6x - (13/2)

Answer 7

13=12x-2y
+ 2y= +2y
13+2y=12x
- 13 = -13
2y=12x-13
/2 =/2
y=6x-13/2

Answer 8

13 = 12x-2y
-12x -12x
-12x+13=-2y
then divide -12x+13 by -2
and -2y by 2.
-12x+13 over 2 = y

Answer 9

13=12x-2y
2y=12x-13
y=12/2(x)-13/2
y = 6x - 13/2

Answer 10

13=12x-2y
-12x -12x
-2y= -12x+13
y= 6x - 2/13