1. -11x^2 + 10x + 20
2. x - 12 = 5
x = 17
3. -12x - 9 - 2 = 7 - 2x + 3
-12x - 11 = -2x + 10
-21 = 10x
x = -21/10
4. multiply everything times 8
2(x + 3) - 12 = x + 4
2x + 6 - 12 = x + 4
2x - 6 = x + 4
x = 10
5. 2(7x - 4) = x + 6
2007-07-11 04:22:22
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answer #1
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answered by Becky M 4
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1) Combine like terms:
-3x2 + 8x – 7x2 + 9 + 2x – x2 + 11
If (-3x2) means -3x^2... then the answer is...
-11x^2+10x+20
2) Solve for x:
5x – 12 = 4x + 5
-4x +12
x=17
3) Solve for x:
-3(4x + 3) – 2 = 7 – 2x + 3
-12x -9 -2 = 7 -2x + 3
-12x - 11 = 10 -2x
+2x +11
-10x = 21
x = -21/10
4) Solve for x:
(x + 3)/4 – 3/2 = (x + 4)/8
Find the least common multiple of the bottom numbers which is 16. Then multiply each fraction by 16.
16* (x+3)/4 - 16* (3/2) = 16* (x+4)/8
4(x+3)-8(3) = 2(x+4)
4x+12-24 = 2x+8
4x-12= 2x+8 -->Then solve for x.
-2x +12
2x = 20
x=10
5) please help me with translating this to an algebra statement; you don't have to solve:
Twice the difference of seven times a number and four yields the same result as the same number increased by six.
2(7x-4)=x+6
**You need to learn how to do algebra! It only gets harder & more complicated!
2007-07-11 04:56:05
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answer #2
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answered by elims4ever 3
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1) Combine like terms:
-3x² + 8x – 7x² + 9 + 2x – x² + 11
There are three properties you NEED to know here.
(1) Associative property of addition: (a+b)+c=a+(b+c)
(2) Commutative property of addition: a+b=b+a
(3) Distributive property of multiplication over addition: a(b+c)=ab+ac
The first two say, in effect, you can add stuff together in any order. Note… it says ADD, it doesn’t say “subtract”.
Next, “like terms” means terms with factors of the same variables with the same exponent. In this case you have terms with x² factors, some with x factors and some with no apparent variable factors.
Because of properties (1) and (2) above, you can rewrite the problem
-3x² + 8x – 7x² + 9 + 2x – x² + 11=
-3x² + -7x² + -x² + 8x + 2x + 9 + 11
Now you have all the x² terms together, all the x terms together, and all the terms without variables together.
Next apply the third property above, the distributive property…
-3x² + -7x² + -x² + 8x + 2x + 9 + 11
= (-3 + -7 + -1)x² + (8 + 2)x + 20… ok, I did a little arithmetic too.
And, now just do the rest of the arithmetic…
= -11x² + 10x + 20
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2) Solve for x:
5x – 12 = 4x + 5
To solve for x, you need to get all the x stuff on one side and everything else on the other…
Add – 4x to both sides to get the x stuff on one side
x – 12 = 5
Add 12 to both sides to get everything else on the other side…
x = 17
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3) Solve for x:
-3(4x + 3) – 2 = 7 – 2x + 3
This one is just like the next one, but the next one has fractions and might look a little harder, so I’ll do that one… then you can do this one… or wait for somebody to do it for you.
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Solve for x:
(x + 3)/4 – 3/2 = (x + 4)/8
Just as with the second problem, you need to get all the x stuff on one side and everything else on the other…
Add –(x+4)/8 to both sides
(x+3)/4 – 3/2 – (x+4)/8 = 0
Now add 3/2 to both sides
(x+3)/4 – (x+4)/8 = 3/2
But we have those blasted fractions… To get rid of them you need to multiply both sides by the lowest common denominator… or at least some common denominator…
Multiply both sides by 8
(2)(x+3) – (x+4) = (4)(3) because (8)(x+3)/4=(8/4)(x+3), (8)(x+4)/8=(8/8)(x+4), and (8)(3/2)=(8/2)(3) There’s a good explanation for that, but it would take too long here. If you want to know, ask me. So, back to the problem…
(2)(x+3) – (x+4) = (4)(3)
Remember that distributive property? Applying it you get
(2)(x+3) – (x+4) = (4)(3)
(2)(x)+(2)(3) + (-x) + (-4) = 12… ok, I did a little arithmetic here too.
That gives us 2x + 6 –x -4 = 12
Applying those three properties again you get
2x – x + 6 – 4 = 12
(2-1)x + 2 = 12
x + 2 = 12
Now this problem is identical to the last step in the second problem.
Add -2 to both sides
x = 10
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5) please help me with translating this to an algebra statement; you don't have to solve:
Twice the difference of seven times a number and four yields the same result as the same number increased by six.
Suppose n is the number.
“Seven time a number” = 7n
“the difference between seven times a number (7n) and 4” = 7n-4
“the (same) number increased by 6” = n+6
The problem says, then, that 7n-4=n+6
This problem now should look familiar.
Get the n stuff on one side and everything else on the other.
Add –n to both sides…
6n – 4 = 6
Get everything else on the other side… add 4 to both sides
6n=10
This is the first time you didn’t wind up with n on the side by itself, the only reason I’m doing this one…
Multiply both sides by 1/6 because (1/6)(6n)=(6)(1/6)n = 1n = n
n=10/6=5/3
2007-07-11 05:03:23
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answer #3
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answered by gugliamo00 7
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Hi,
------------------------------------
All these problems involve gathering the like terms together.
which involves transferring of terms from LHS to RHS and vice versa in an equation. The rules to follow the transfer are
Addition term ( +ve term) becomes subtraction term (-ve term) and vice versa
Multiplier (numerator) becomes divisor (denominator) and vice versa. See the following examples
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1) Combine like terms:
-3x2 + 8x – 7x2 + 9 + 2x – x2 + 11
= -3x2 - 7x2 -x2 + 8x + 2x + 9 + 11
= - 11x2 + 10x + 20
2) Solve for x:
5x – 12 = 4x + 5
5x - 4x = + 5 +12
x = 17
3) Solve for x:
-3(4x + 3) – 2 = 7 – 2x + 3
-12x - 9 - 2 = 7 - 2x + 3
7 -2x + 3 = - 12x - 9 - 2
12x - 2x = - 9 - 2 - 7 - 3
10x = -21
x = - 21/10 = - 2 1/10
4) Solve for x:
(x + 3)/4 – 3/2 = (x + 4)/8
[(x + 3) - 6]/4 = (x + 4)/8.............| Taking LCM (2, 4) = 4 in LHS
8[(x + 3) - 6] = 4(x + 4)
2[(x + 3) - 6] = (x + 4)
2x + 6 -12 = x + 4
2x - x = 4 - 6 + 12
x = 10
5) let the number be x
LHS = 2(7x - 4)
RHS = x + 6
2(7x - 4) = x + 6
good luck
2007-07-11 04:24:20
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answer #4
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answered by sudhakarbabu 3
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-3x2 + 8x – 7x2 + 9 + 2x – x2 + 11
= -11x^2 +10x +20
5x – 12 = 4x + 5
5x - 4x = 5+12
x = 17
-3(4x + 3) – 2 = 7 – 2x + 3
-12x -9 -2 = 7 -2x + 3
-12x +2x = 7 +3 +9+2
-10x = 21
x = -2.1
Let x = the number
Then 2(7x-4) = x+6
2007-07-11 04:27:57
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answer #5
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answered by ironduke8159 7
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1) - 3x^2 + 8x - 7x^2 + 9 + 2x +11
- 10x^2 + 10x + 20
2) 5x - 12 = 4x - 5
5x - 4x = 12 - 5
x = 7
3) - 3(4x + 3) - 2 = 7 - 2x + 3
- 12x - 9 - 2 = 10 - 2x
- 12x + 2x = 10 + 9 + 2
- 10x = 21
x = 21/(-10)
x = - 2.1
4) (x + 3) / 4 - 3/2 = (x + 4) / 8
1/4x + 3/4 - 3/2 = 1/8x + 1/2
1/4x - 1 5/12 = 1/8x + 1/2
1/4x - 1/8x = 1/2 + 1 5/12
1/8x = 1 11/12
x = (1 11/12) / (1/8)
x = 15 1/3
5) 2 * (7x - 4) = x + 6
14x - 8 = x + 6
14x - x = 6 + 8
13x = 14
x = 1 1/13
2007-07-15 00:46:31
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answer #6
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answered by Jun Agruda 7
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1) Combine the x squared terms: -3x^2 -7x^2 -x^2 = -11x^2, then combine the x terms: +8x +2x = +10x, then finally the numerical terms: +9 +11 = +20. Put them together into one expression: -11x^2 + 10x +20.
2) Subtract 4x from both sides, leaving x - 12 = 5. Add 12 to both sides, leaving x = 17.
3) Simplify on both sides: -12x - 9 - 2 = 10 - 2x. Add 12x to both sides: -11 = 10 + 10x. Subtract 10 from both sides: -21 = 10x. Divide both sides by 10: -2.1 = x.
4) Multiply both sides by the LCD of 8: 2(x+3) - 12 = x + 4. Simplify the left side: 2x + 6 - 12 = 2x - 6 = x + 4. Subtract x from both sides, x - 6 = 4. Add 6 to both sides, x = 10.
5) Let x be the number. 2(7x - 4) = x + 6.
2007-07-11 04:33:09
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answer #7
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answered by TitoBob 7
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1: = -6 -14 +9 +11 +8x +2x -x^2 = 10x - x^2
2. 5x - 12 = 4x + 5
5x - 17 = 4x
5x - 17 - 4x = 0 = 9x - 17.
Therefore, 9x = 17, therefoe, x = 17/9 = 1.888...
3. -12x -9 -2 = 10 - 2x
-12x - 21 = -2x
12x + 21 = 2x
Therefore, 10x = -21, x =-2.1
4. (1/4)x + 3/4 - 6/4 = (1/8)x + 1/2
(1/4)x -3/4 = (1/8)x + 1/2
(1/4)x - (1/8)x = 1/2 + 3/4
(1/8)x = 5/4
x = 40/4 = 10
5. 7n-4 = 6n Though you need to incorporate a symbol to represent the fact that 7n-4 is a positive number, (ie, if 7n-4 = 6, then it represents 6. If 7n-4 = -6, then it still represents 6). I do not recall the symbol that represents this transformation.
2007-07-11 04:32:50
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answer #8
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answered by Ian I 4
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-3x2-x2-7x2 +8x+2x+9+11=-12x2 +10x+20
5x-4x=5+12 => x=17
-12x-9-2= -2x+10=> -12x-11 =-2x+10=> -12x+2x=10+11=>
-10x=21=>x= -(21/10)
(x+3-4)/4=(x+4)/8
(x-1)/4=(x+4)/8 cross mulltiplying
8x-8 =4x+16
8x-4x=16+8
4x=24
x=24/4
x=6
i m too confused about the 5 question
2007-07-11 04:31:50
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answer #9
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answered by Anonymous
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um wow ok for the 1st one 35 is 70% of what. what u do is placed 70 over a hundred using fact its 70% ceremony? and that equals 35 out of a variety or X. so ceremony now u have 70/a hundred = 35/X so what do u do to 70 to get 35? divide by ability of two. so u do a similar with the a hundred so its then 50. so 35/50. so 35 is 70% of fifty. a hundred and forty four divided by ability of -8 = -18 something in parentisees immediately next to a variety is multiplication so 12x-12=-a hundred and forty four. ok fractions into percents. we could sayy a million/4. a million/4=x/a hundred cuz proportion is out of a hundred. so as which ability it could be 25% using fact a million/4 equals 25/a hundred.. then decimals. think of of it as proportion basicaly. yet instead of a hundred its a million.00. so if the fraction is a million/4 then the share is 25% so as which ability itd in basic terms be .25 gett it? digital mail if u have anymore questions
2016-10-19 03:53:22
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answer #10
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answered by Anonymous
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