# Solve absolute value inequality : |3(x-1)|+2\le 20

Solve absolute value inequality :
$|3\left(x-1\right)|+2\le 20$
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Step 1
Given inequality is
$|3\left(x-1\right)|+2\le 20$
Step 2
$|3\left(x-1\right)|+2\le 20$
Subtract 2 from both sides,
$|3\left(x-1\right)|+2-2\le 20-2$
$|3\left(x-1\right)|\le 18$
We know, if $|x|\le a$, then
Hence, given inequality becomes,
$-18\le 3\left(x-1\right)\le 18$
Divide all sides by 3,
$-\frac{18}{3}\le \frac{3\left(x-1\right)}{3}\le \frac{18}{3}$
$-6\le x-1\le 6$
$-6+1\le x-1+1\le 6+1$
$-5\le x\le 7$
Hence, the solution is .