Which inequality is equivalent to |x - 5| ≤ 3?

The inequality $|x - 5| \leq 3$ says the distance from $x$ to 5 is at most 3. So $x$ lies between $5 - 3$ and $5 + 3$, which gives $2 \leq x \leq 8$, choice A. Equivalently, $-3 \leq x - 5 \leq 3$, then add 5 to all three parts. Choice B ($-2 \leq x \leq 8$) adds 5 to the right bound but mishandles the left, getting $-2$ instead of 2. Choice C ($2 \leq x \leq 3$) uses 3 as the upper bound without adding 5. Choice D describes the outside of the interval, which would be the solution of $|x - 5| \geq 3$.