Question

Which inequality represents all the solutions of -2(3x+6) ≥ 4(x + 7)?

Options:
A. x ≤ -4
B. x ≤ 4
C. x ≥ -8
D. x ≥ 8

Answer 1

To find the solution to the inequality -2(3x+6) ≥ 4(x + 7), distribute the -2, collect like terms, divide by -10 and reverse the inequality sign to get the solution x ≤ -4, which corresponds to option A.

Step-by-step explanation:

To solve the inequality -2(3x+6) ≥ 4(x + 7), follow these steps:

1. Distribute the -2 to the terms inside the parentheses: -6x - 12 ≥ 4x + 28.
2. Move all terms with x to one side and constant terms to the other side to collect like terms: -6x - 4x ≥ 28 + 12, which simplifies to -10x ≥ 40.
3. Divide both sides by -10, remembering to reverse the inequality symbol because you are dividing by a negative number: x ≤ -4.

This means the correct inequality for all the solutions of the original inequality is x ≤ -4, which corresponds to option A.