If |x-2| x-2 0, then: 1. x [2, ) 2. x (2, ) 3. x (- ,2) 4. x (- ,… - Vidyadip

Question

If $\frac{|\text{x}-2|}{\text{x}-2}\geq0,$ then:

$\text{x}\in[2,\infty)$
$\text{x}\in(2,\infty)$
$\text{x}\in(-\infty,2)$
$\text{x}\in(-\infty,2]$

✓

Answer

[-7, 3]

Solution:

$|\text{x}+2|\leq5$

$\Rightarrow-5\leq\text{x}+2\leq5$

$\Rightarrow-5-2\leq\text{x}+2-2\leq5-2$

$\Rightarrow-7\leq\text{x}\leq3$

$\Rightarrow\text{x}\in[-7,3]$

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