1962 AHSME Problems/Problem 33

Problem

The set of $x$ -values satisfying the inequality $2 \leq |x-1| \leq 5$ is:

$\textbf{(A)}\ -4\leq x\leq-1\text{ or }3\leq x\leq 6\qquad$

$\textbf{(B)}\ 3\leq x\leq 6\text{ or }-6\leq x\leq-3\qquad\textbf{(C)}\ x\leq-1\text{ or }x\geq 3\qquad$

$\textbf{(D)}\ -1\leq x\leq 3\qquad\textbf{(E)}\ -4\leq x\leq 6$

Solution

This inequality can be split into two inequalities: $2\le x-1\le5$ or $2\le1-x\le5$ . Solving for x gives $3\le x\le6$ or $-4\le x\le-1$ . $\boxed{\textbf{(A)}}$

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1962 AHSME Problems/Problem 33

Problem

Solution