Question

Which inequality represents all the solutions of 2(3x+6) ≤ 24 - 7x?

A) x ≤ 4
B) x ≥ -8
C) x ≤ 28
D) x ≥ 8

Answer 1

To solve the inequality 2(3x+6) ≤ 24 - 7x, distribute 2, combine like terms, isolate x, and solve.

Step-by-step explanation:

To solve the inequality 2(3x+6) ≤ 24 - 7x, we need to simplify and isolate the variable x. First, distribute 2 to (3x+6) to get 6x+12 ≤ 24 - 7x. Then, combine like terms by adding 7x to both sides, yielding 13x + 12 ≤ 24. Next, subtract 12 from both sides to obtain 13x ≤ 12. Finally, divide both sides of the inequality by 13 to get x ≤ 12/13.

Therefore, the correct inequality that represents all the solutions is x ≤ 12/13.