QUESTION 1
The given equation is
[tex]2.5(10 - x) + 10 = 72 - 1.5(5x + 12)[/tex]
Clear the decimal by multiplying through by 10 to get,
[tex]25(10 - x) + 100 = 720 - 15(5x + 12)[/tex]
Expand the bracket using the distributive property to get;
[tex]250 - 25x + 100 = 720 - 75x - 180[/tex]
Group similar terms to get,
[tex] - 25x + 75x = 720 - 250 - 100 - 180[/tex]
[tex]50x = 720 - 530[/tex]
[tex]50x = 190[/tex]
Divide through by 50 to get,
[tex]x = \frac{190}{50} [/tex]
[tex]x = \frac{19}{5} [/tex]
QUESTION 2
We want to solve the inequality,
[tex]16x \: > \: 12(2x - 6) - 24[/tex]
We expand the bracket using the distributive property to obtain,
[tex]16x \: > \: 24x - 72 - 24[/tex]
Group similar terms to get,
[tex]16x - 24x \: > \: - 72 - 24[/tex]
Simplify to get,
[tex] - 8x \: > \: - 96[/tex]
We divide both sides of the inequality by -8 and reverse the sign to obtain,
[tex]x \: < \: \frac{ - 96}{ - 8} [/tex]
[tex]x \: < \: 12[/tex]
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.
