Solve: |x-1| 5, |x| 2 - Vidyadip

MCQ

Solve: $|\text{x}-1|\leq 5, |\text{x}|\geq2$

A
$[2, 6]$
B
$[-4, -2]$
✓
$[-4, -2]\cup[2, 6]$
D
$\text{None of these}$

✓

Answer

Correct option: C.

$[-4, -2]\cup[2, 6]$

Given, $|\text{x}-1|\leq 5, |\text{x}|\geq2$
$\Rightarrow-(5\leq(\text{x} – 1)\leq5), (\text{x}\leq -2 \text{or} \text{x} \geq 2)$
$\Rightarrow-(4\leq\text{x}\leq6), (\text{x}\leq-2 \text{or}\text{x}\geq 2)$
Now, required solution is.
$\text{x}\in[-4, -2]\cup[2, 6]$

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