Solve: 1 |x – 1| 3 - Vidyadip

MCQ

Solve: $1\leq|\text{x} – 1|\leq3$

A
$\big[-2,0\big]$
B
$\big[2,4\big]$
✓
$\big[-2,0\big]\cup\big[2,4\big]$
D
$\text{None of these}$

✓

Answer

Correct option: C.

$\big[-2,0\big]\cup\big[2,4\big]$

Given, $ 1\leq|\text{x} – 1|\leq3$
$\Rightarrow-3\leq(\text{x} – 1)\leq-1 $ or $1\leq(\text{x}-1)\leq3$
i.e. the distance covered is between $1$ unit to $3$ unit.
$\Rightarrow-2\leq \text{x}\leq0$ or $2\leq\text{x}\leq4$
Hence, the solution set of the given inequality is
$\text{x}\in\big[-2, 0\big]\cup\big[2, 4\big]$

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