Which of the following is equivalent to -3x + 7 ≤ 22?

Start with $-3x + 7 \leq 22$. Subtract 7 from both sides: $-3x \leq 15$. Now divide both sides by $-3$. Dividing by a negative number reverses the inequality, so $x \geq -5$, choice D. Test $x = 0$: $7 \leq 22$ is true, and $0 \geq -5$ is true, which confirms the direction. Choice A ($x \leq -5$) keeps the original direction of the inequality and flips only the sign of the number. Choice B ($x \geq 5$) and choice C ($x \leq 5$) both lose the negative sign on the boundary value, which results from dividing 15 by 3 instead of by $-3$.