Question

Solve the inequality 32(x + 2) ≤ -12(x - 8).

1) x ≤ 12
2) x is less than or equal to 1/2
3) x ≤ -12
4) x is less than or equal to -1/2
5) x ≥ -12
6) x is greater than or equal to -1/2
7) x ≥ 12

Answer 1

After solving the inequality 32(x + 2) ≤ -12(x - 8), we find that x ≤ 8/11, which is approximately 0.727. None of the provided options match this solution.

Step-by-step explanation:

To solve the inequality 32(x + 2) ≤ -12(x - 8), first expand both sides to remove the parentheses:

• 32x + 64 ≤ -12x + 96

Next, move all x terms to one side and constants to the other side:

• 32x + 12x ≤ 96 - 64
• 44x ≤ 32

Divide both sides by 44 to isolate x:

• x ≤ 32/44
• x ≤ 8/11

Since 8/11 is approximately 0.727, the inequality implies that x can be any value less than or equal to approximately 0.727. Therefore, none of the multiple-choice options provided are correct for this inequality.