Question

solve the following inequality for b. write your answer in simplest form.
10 - 3(-5b - 6) ≤ -9b - 5 + 8

Explanation:

Step1: Expand the left - hand side

$10-3(-5b - 6)=10 + 15b+18=15b + 28$

Step2: Simplify the right - hand side

$-9b-5 + 8=-9b+3$

Step3: Rewrite the inequality

$15b + 28\leq -9b+3$

Step4: Add 9b to both sides

$15b+9b + 28\leq -9b+9b+3$
$24b+28\leq3$

Step5: Subtract 28 from both sides

$24b+28 - 28\leq3 - 28$
$24b\leq - 25$

Step6: Divide both sides by 24

$b\leq-\frac{25}{24}$

Answer:

$b\leq-\frac{25}{24}$