Question

Please check my answers for me.

Solve for x. Show each step of the solution.



2.5(10 - x) + 10 = 72 – 1.5(5x + 12)

25-2.5x+10=72-7.5x-18


35-2.5x=54-7.5x

-2.5x+7.5x=54-35

5x=19

x=19/5


Solve the inequality for x. Show each step of the solution.

16x > 12(2x – 6) – 24

16x>24x-72-24

16x>24x-96

16x-24x>-96

-8x>-96 x<12


Justify each step of the solution by stating the property that was used to get to each step.

• Given: 4(-6x – 3) + 24x = -72x + 132

• Distributive property: -24x – 12 + 24x = -72x + 132

• Combine like terms: –12 = -72x + 132

• Addition property of equality: -144 = -72x

• Division property of equality: 2 = x

Answer 1

QUESTION 1

The given equation is


`2.5(10 - x) + 10 = 72 - 1.5(5x + 12)`
Clear the decimal by multiplying through by 10 to get,


`25(10 - x) + 100 = 720 - 15(5x + 12)`

Expand the bracket using the distributive property to get;


`250 - 25x + 100 = 720 - 75x - 180`

Group similar terms to get,


`- 25x + 75x = 720 - 250 - 100 - 180`


`50x = 720 - 530`


`50x = 190`

Divide through by 50 to get,


`x = (190)/(50)`


`x = (19)/(5)`

QUESTION 2

We want to solve the inequality,


`16x \: > \: 12(2x - 6) - 24`

We expand the bracket using the distributive property to obtain,


`16x \: > \: 24x - 72 - 24`

Group similar terms to get,


`16x - 24x \: > \: - 72 - 24`

Simplify to get,


`- 8x \: > \: - 96`

We divide both sides of the inequality by -8 and reverse the sign to obtain,


`x \: < \: ( - 96)/( - 8)`


`x \: < \: 12`

QUESTION 3


Step 1.

Given:4(-6x – 3)+24x= -72x + 132

Step 2.

Distributive property:
-24x – 12 + 24x = -72x + 132

Step 3.

Combine like terms:
–12 = -72x + 132

Step 4.

Addition property of equality:

-144 = -72x

Step 5.

Division property of equality:

2=x

All the properties stated are correct.