Question

Please check my answers for me.

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,

$x = \frac{190}{50}$

$x = \frac{19}{5}$

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,

$x \: < \: \frac{ - 96}{ - 8}$

$x \: < \: 12$

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.