Question

Solve the following compound inequality.

5x + 7 ≤ -3 OR 3x - 4 ≥ 11

A. -2 ≤ x ≤ 5

B. x ≤ -2 OR x ≥ 5

C. x ≤ -15 OR x ≥ 12

D. x ≥ 5

Thank you!

Answer 1

B

Explanation:

We have the compound inequality:

`5x+7\leq-3 \text{ or } 3x-4\geq 11`

Since this is an “OR” inequality, we can solve each inequality individually. So:

1)

We have:

`5x+7\leq-3`

Subtract 7 from both sides:

`5x\leq -10`

Divide both sides by 5:

`x\leq-2`

So, the first solution is above.

2)

We have:

`3x-4\geq 11`

Add 4 to both sides:

`3x\geq15`

Divide both side by 3:

`x\geq5`

Our second solution is above.

Therefore, our solution is:

`x\leq -2 \text{ or } x\geq5`

Since our original inequality is “OR,” our solution set remains an “OR.”

Hence, our answer is B.