# Solve absolute value inequality. |3(x-1)/4|<6

Solve absolute value inequality.
|3(x-1)/4|<6
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xandir307dc

Step 1
we have to solve the given absolute inequality:
|3(x−1)/4|<6
as we know that if |x| then $x\in \left(-a,a\right)$ that implies -a therefore,
if |3(x-1)/4|<6 then $-6<\frac{3\left(x-1\right)}{4}<6$
Step 2
therefore,
$-6<\frac{3\left(x-1\right)}{4}<6$
$-6×4<3\left(x-1\right)<6×4$
-24<3 (x-1)<24
$-\frac{24}{3}
-8< x-1 <8
-8+1 -7 therefore the solution of the given inequality

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lovagwb
Step 1
Given inequality is $|\frac{3\left(x-1\right)}{4}|<6$
Simplify the given inequality as follows.
$|\frac{3\left(x-1\right)}{4}|<6$
$-6<\frac{3\left(x-1\right)}{4}<6$
-24<3(x-1)<24
Step 2
On further simplifications,
$⇒-24<3\left(x-1\right)$
3x-3>-24
3x>-24+3
3x>-21
x>-7
$⇒3\left(x-1\right)<24$
3x-3<24
3x<24+3
3x<27
x<9
Thus, the solution is -7<x< 9 or (-7,9).