If (|x -1| \<= 1), then | Mathematics | SolveeIt

Question

If $|x -1| \leq 1$ , then

$x \in [1,3]$

$x \in (1,3)$

$x \in [-1,3)$

$x \in (-1,3)$

Answer

$x \in [1,3]$

Explanation

Solution

We have.
$|x-2| \leq 1$
$\Rightarrow-1 \leq x-2 \leq 1$
$\Rightarrow -1+2 \leq x-2+2 \leq 1+2$
$\Rightarrow 1 \leq x \leq 3$
$\therefore x \in[1,3]$
Note Correction in the question
$|x-2| \leq 1$

Mathematics Question on linear inequalities

Solution