Question

solve the linear inequality for a. write your answer in inequality notation. 2(-9a - 16) - 32 ≥ 18a + 80

Explanation:

Step1: Expand the left side

$2(-9a - 16) - 32 = -18a - 32 - 32$

Step2: Simplify the left side

$-18a - 32 - 32 = -18a - 64$

Step3: Rearrange terms to isolate $a$

$-18a - 64 \geq 18a + 80$
$-18a - 18a \geq 80 + 64$

Step4: Combine like terms

$-36a \geq 144$

Step5: Divide by -36, reverse inequality

$a \leq \frac{144}{-36}$
$a \leq -4$

Answer:

$a \leq -4$