Question

满足不等式 $2\le|x-1|\le5$ 的 $x$ 值集合为：

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

$-4\le x\le-1$ 或 $3\le x\le6$

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

$3\le x\le6$ 或 $-6\le x\le-3$

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

$x\le-1$ 或 $x\ge3$

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

$-1\le x\le3$

$-4\le x\le6$

将该不等式理解为到 $1$ 的距离介于 $2$ 与 $5$ 之间

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

分别解 $2\le x-1\le5$ 和 $-5\le x-1\le-2$

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

当 $x-1\ge0$ 时，界限给出 $3\le x\le6$ 。当 $x-1\le0$ 时，给出 $-4\le x\le-1$ 。解集是这两个区间的并集。

所以正确答案是 A。

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.