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

QUESTION 1

The given equation is


Clear the decimal by multiplying through by 10 to get,



Expand the bracket using the distributive property to get;



Group similar terms to get,







Divide through by 50 to get,





QUESTION 2

We want to solve the inequality,



We expand the bracket using the distributive property to obtain,



Group similar terms to get,



Simplify to get,



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





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.