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!

Question

asked Oct 15, 2021 29.9k views

1 Answer

Csterling · Answer 1 · 2021-10-22T11:46:24+0000

Answer:

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.