1962 AMC 12 Problem 33

Attempt Problem 33 of the 1962 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1962 AMC 12 solutions, or check the answer key.

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33.

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

Answer: A

Concepts:absolute value inequality

Difficulty rating: 1180

Small hint:

Interpret the inequality as distances from

1

between

2

and

5

Big hint:

Solve

2\le x-1\le5

and

-5\le x-1\le-2

Solution:

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.