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Inequalities involving modulus function

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Question

If $| x - 1 | \leq 2$
then, the value of x is more than equal to and less than equal to .

A

-2

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B

-1

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C

-3

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D

1

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E

2

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F

3

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Solution

The correct options are
B -1
F 3
$| x - 1 | \leq 2 \Rightarrow - 2 \leq x - 1 \leq 2 \Rightarrow - 2 + 1 \leq x - 1 + 1 \leq 2 + 1 \Rightarrow - 1 \leq x \leq 3$

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