|3(x-1)/4|<6

fertilizeki
2021-12-19
Answered

Solve absolute value inequality.

|3(x-1)/4|<6

|3(x-1)/4|<6

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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

if |3(x-1)/4|<6 then

Step 2

therefore,

-24<3 (x-1)<24

-8< x-1 <8

-8+1 -7 therefore the solution of the given inequality

lovagwb

Answered 2021-12-21
Author has **50** answers

Step 1

Given inequality is$\left|\frac{3(x-1)}{4}\right|<6$

Simplify the given inequality as follows.

$\left|\frac{3(x-1)}{4}\right|<6$

$-6<\frac{3(x-1)}{4}<6$

-24<3(x-1)<24

Step 2

On further simplifications,

$\Rightarrow -24<3(x-1)$

3x-3>-24

3x>-24+3

3x>-21

x>-7

$\Rightarrow 3(x-1)<24$

3x-3<24

3x<24+3

3x<27

x<9

Thus, the solution is -7<x< 9 or (-7,9).

Given inequality is

Simplify the given inequality as follows.

-24<3(x-1)<24

Step 2

On further simplifications,

3x-3>-24

3x>-24+3

3x>-21

x>-7

3x-3<24

3x<24+3

3x<27

x<9

Thus, the solution is -7<x< 9 or (-7,9).

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