Question

If the inequality -2(x + 10) ≤ 16 is true, which of these inequalities is also true?

a) x + 10 ≥ -8
b) x + 10 < -8
c) x + 10 > -8
d) x + 10 = 8

Answer 1

To solve the inequality -2(x + 10) ≤ 16 and find a true statement, we isolate the variable x and check which given inequality is also true. The correct answer is a) x + 10 ≥ -8.

Step-by-step explanation:

To solve the inequality -2(x + 10) ≤ 16, we need to isolate the variable x. First, distribute the -2 to both terms inside the parentheses: -2x - 20 ≤ 16. Then, add 20 to both sides of the inequality: -2x ≤ 36. To isolate x, divide both sides of the inequality by -2, remembering to flip the inequality sign when dividing by a negative number: x ≥ -18.

Now, let's check which of the given inequalities is also true. The inequality x + 10 ≥ -8 is true because if we substitute x = -18, we get -18 + 10 ≥ -8, which simplifies to -8 ≥ -8. Therefore, the correct answer is a) x + 10 ≥ -8.