Question

The set of $x$ -values satisfying the inequality $2\le|x-1|\le5$ is:

$-4\le x\le-1$ or $3\le x\le6$

$3\le x\le6$ or $-6\le x\le-3$

$x\le-1$ or $x\ge3$

$-1\le x\le3$

$-4\le x\le6$

Interpret the inequality as distances from $1$ between $2$ and $5$

Solve $2\le x-1\le5$ and $-5\le x-1\le-2$

For $x-1\ge0,$ the bounds give $3\le x\le6.$ For $x-1\le0,$ they give $-4\le x\le-1.$ The solution is the union of these two intervals.

Thus, the correct answer is A.