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

fertilizeki 2021-12-19 Answered
Solve absolute value inequality.
|3(x-1)/4|<6
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Expert Answer

xandir307dc
Answered 2021-12-20 Author has 35 answers

Step 1
we have to solve the given absolute inequality:
|3(x−1)/4|<6
as we know that if |x| then x(a,a) that implies -a therefore,
if |3(x-1)/4|<6 then 6<3(x1)4<6
Step 2
therefore,
6<3(x1)4<6
6×4<3(x1)<6×4
-24<3 (x-1)<24
243<x1<243
-8< x-1 <8
-8+1 -7 therefore the solution of the given inequality |3x14|<6 is x(7,9)

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lovagwb
Answered 2021-12-21 Author has 50 answers
Step 1
Given inequality is |3(x1)4|<6
Simplify the given inequality as follows.
|3(x1)4|<6
6<3(x1)4<6
-24<3(x-1)<24
Step 2
On further simplifications,
24<3(x1)
3x-3>-24
3x>-24+3
3x>-21
x>-7
3(x1)<24
3x-3<24
3x<24+3
3x<27
x<9
Thus, the solution is -7<x< 9 or (-7,9).
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