Question

If $|2-\left|\right[x]-1||\le 2$, then $x$ belongs to the solution set (where [.] represents greatest integer function)

• A. $[-3,6)$
• B. $[-4,6)$
• C. $[-3,7)$
• D. $[-3,6]$

Answer 1

The correct option is A $[-3,6)$

Given,

$|2-|\left[x\right]-1||\le 2$

$⟹-2\le 2-|\left[x\right]-1|\le 2$

$⟹-4\le -|\left[x\right]-1|\le 0$

$⟹0\le |\left[x\right]-1|\le 4$

$⟹-4\le \left[x\right]-1\le 4$

$⟹-3\le \left[x\right]\le 5$

$⟹x$ belongs to $[-3,6)$

Hence, the answer is option $A$