Solve absolute value inequality : |2-\frac{x}{2}|-1\le 1

pro4ph5e4q2 2021-12-06 Answered
Solve absolute value inequality : $|2-\frac{x}{2}|-1\le 1$
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Expert Answer

pendukke
Answered 2021-12-07 Author has 9 answers

Step 1
Given: $|2-\frac{x}{2}|-1\le 1$
for finding solution of it, we simplify given inequality
Step 2
so,
$|2-\frac{x}{2}|-1\le 1$
$|2-\frac{x}{2}|\le 1+1$
$|\frac{2\left(2\right)-x}{2}|\le 2$
$|\frac{4-x}{2}|\le 2$
$\frac{|x-4|}{2}\le 2$
$|x-4|\le 2\left(2\right)$
$|x-4|\le 4$
we know that
if,
Step 3
similarly,

so, solution of given inequality will be $x\in \left[0,8\right]$
hence, solution will be $x\in \left[0,8\right]$.

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