Algebra equation help...?

Question

I agreed to help my kid with his homework..... I have no clue wat im doing to be honest so could someone please help me out and show me how to work these out so I can show him? Any help would be grateful

a. 3-3p=3(2p-8)

b. 3x/4=2x-15

c. x²+9x+14=0

d. x²-9=0

Answer 1

a) 3-3p=6p-24
9p=27
p=3
b) 3x=4(2x-15)
3x=8x-60
5x=60
x=12
c)x^2 +7x+2x+14=0
x(x+7)+2(x+7)=0
x= -7or x= -2
d) (x-3)(x+3)=0
x=3orx= -3

Answer 2

A. *Eliminate parenthesis: use distribution > multiply 3 with both terms in the parenthesis ...

3 - 3p = 3(2p) - 3(8)
3 - 3p = 6p - 24

First: subtract 6p from both sides ...

3 - 3p - 6p = 6p - 6p - 24
3 - 9p = -24

*Subtract 3 from both sides ...

3 - 3 - 9p = -24 - 3
- 9p = -27

Sec: solve for "p" by isolating it on one side > divide both sides by - 9 ...

- 9p/-9 = -27/-9
p = 3

B. *Eliminate the fraction > multiply the denominator by everything ...

4(3x/4) = 4(2x - 15)

First: cross cancel "like" terms and distribute 4 with both terms in the parenthesis ...

3x = 8x - 60

Sec: subtract 8x from both sides...

3x - 8x = 8x - 8x - 60
-5x = -60

Third: divide both sides by -5...

-5x/-5 = -60/-5
x = 12

C. *Factor: multiply the 1st and 3rd coefficient to get 14. Find two numbers that give you 14 when multiplied and 9 (middle coefficient) when added/subtracted. The numbers are: 2, 7

First: rewrite the equation with the new middle numbers and group "like" terms ...

(x² + 2x) + (7x + 14) = 0

Sec: factor both sets of parenthesis >

x(x + 2) + 7(x + 2) = 0
(x + 2)(x + 7) = 0

Third: solve for both "x" variables > place both sets to equal "0" ...

x + 2 = 0
x + 2 - 2 = 0 - 2
x = -2

x + 7 = 0
x + 7 - 7 = 0 - 7
x = - 7

x = -2, 7

D. (x+3)(x-3) = 0
x + 3 = 0
x + 3 - 3 = 0 - 3
x = - 3

x - 3 = 0
x - 3 + 3 = 0 + 3
x = 3

x = -3, 3

Answer 3

Ok. You want to isolate the 'like terms' on one side of the equation so that you can the solve.

so, with

a) 3-3p=3(2p-8)

Multiply out (of the brackets) the r.h.s. (right hand side) to simplify:

3-3p = 6p-24

Get both 'p' terms on one side by adding and subtracting:

6p+3p = 3+24

add them up:

9p = 27

p = 27/9
p = 3

b) 3x/4=2x-15

Multipy it all by 4 to get

3x = 8x-60

Get both x terms on the same side:

3x-8x = -60

-5x = -60

Multiply both sides by -1 to get

5x = 60

x = 60/5

x = 12

I don't have time to explain c) I'm afraid.

d) x²-9=0

Get x² on it's own:

x² = 9

x= square root of 9

x= 3 or -3

I hope those help. I'm at work so couldn't go into too much detail.

Answer 4

Step by step instructions.

a. First, multiply through to get rid of brackets, using a(b+c) = ab + ac

3 - 3p = 6p-24

Add 3p to both sides
3 = 9p-24

Add 24 to both sides

27 = 9p

Divide both sides by 9
3 = p

=====

b. Multiply both sides by 4

3x = 8x - 60
Subtract 8x from both sides
-5x = -60

Divide both sides by -5
x = 12

===========

c. Factor. You need to find two numbers that multiply out to 14 and add to 9. Those are 2 and 7

(x+7)(x+2) = 0

Set both factors equal to zero, as either one is a legitimate answer (ab=0 means a=0 or b=0)

(x+7) = 0 or (x+2) =0

x = -7 or x = -2 is the answer

==============

d. You have to know that (a² - b²) = (a+b)(a-b)

This factors to:
(x+3)(x-3) = 0
set both factors equal to zero, solve as above

x = -3 or x=3

typically written
x=±3

Answer 5

a. 3 - 3p = 3*2p - 3*8 {Multiply through by 3)
3 - 3p = 6p - 24 { do the math }
3 + 24 = 6p + 3p { add 3p + 24 to both sides }
27 = 9p { combine like terms }
p = 3 { divide both sides by 9 }

Now do the same things with the other four. You can add, subtract, multiply and divide both sides of an equation by the same things, and the equation will remain true.

Answer 6

Please excuse my dear Aunt Sally! (Parentheses, exponents, multiplication/division, addition/subtraction) in that order, so for a)
3-3p=6p-24; then combine like terms
3+24 = 6p +3p (signs change when they cross the = sign):
add or subtract:
27=9p; Simplify by dividiing both sides by 9:
3=p
b) Is the same idea, but first multiply everything by 4 to get rid of the fraction:3x=8x-60; then continue
c) find the roots of x by factoring: (x+7)(x+2) this is called foiling
d)this is factoring too but it is a perfect square so no center term! Good luck!

Answer 7

For a.

First, distribute the 3 by multiplying the 3 times 2p and -8 to get:
3-3p=6p-24
Then add 3p to both sides of the equation to get:
3=9p-24
Then add 24 to both sides:
27=9p
Lastly, divide both sides by 9:
3=p

For b.

First, multiply both sides of the equation by 4:
3x=8x-60
Then, subtract 8x from both sides:
-5x= -60
Then, divide both sides by -5:
x=12

For c.

First factor the trinomial on the left side:
(x+2)(x+7)=0
Then, set each factor on the left hand side equal to zero:
x+2=0 and x+7=0
Finally, subtract 2 from both sides in the first equation and 7 from both sides of the second one:
x= -2 and x= -7

For d.

First, add 9 to both sides:
x squared=9
Then, square root both sides:
x= 3 or -3

Answer 8

a.

3-3p=3(2p-8)
3-3p=6p-24
27=9p
p=27/9
p=3

b.
3x/4=2x-15
3x=2x-15(4)
3x=8x-60
-5x= -60
x=12

d.

x2 - 9 = 0
x2 = 9
x = 3

Answer 9

a)3-3p=3(2p-8)
Use distributive property:
3-3p=6p-24

Subtract 6p from both sides:
3-9p=-24

Subtract 3 from both sides:
-9p=-27

Divide -9 from both sides:
p=3

Check:
3-3(3)=3(2(3)-8)
3-9=3(6-8)
3-9=3(-2)
-6=-6

b)3x/4=2x-15
Multiply both sides by 4 to get rid of the fractions:
4(3x/4)=4(2x-15)
3x=8x-60

Subtract 8x from both sides:
-5x=-60

Divide -5 from both sides:
x=12

Check:
3(12)/4=2(12)-15
36/4=24-15
9=9

c)x²+9x+14=0
Factor them out:
(x+7)(x+2)=0
x+7=0
x+2=0
x=-7 or -2

d)x²-9=0
Factor this out:
(x+3)(x-3)=0
x+3=0
x-3=0
x=±3

Check:
(3)²-9=0
9-9=0
0=0

(-3)²-9=0
9-9=0
0=0

I hope this helps and I hope your kid does well in his math class!

Answer 10

a. 3-3p= 6p-24
27=9p
3=p
b. 3x=8x-60
-5x=-60
x=12
c. (x+7) (x+2)
x= -7, -2
d. x²=9
x= 3, -3