Linda Seales

## Answered question

2021-12-14

Solve.
$|\frac{6x+2}{4}|>4$

### Answer & Explanation

Timothy Wolff

Beginner2021-12-15Added 26 answers

Step 1
Apply the properties of absolute value function, to remove the modulus sign in the given inequality.
If |x|>a, a>0 then x>a or -x>a.
$|\frac{6x+2}{4}|>4$
$\left(\frac{6x+2}{4}\right)>4$...(1)
$-\left(\frac{6x+2}{4}\right)>4$
$\left(\frac{6x+2}{4}\right)<-4$...(2)
Step 2
To find the value of x, multiply by 4, then subtract 2 and divide by 6 on both sides of the inequalities (1) and (2).
$\frac{6x+2}{4}>4$
$\left(\frac{6x+2}{4}\right)\left(4\right)>\left(4\right)\left(4\right)$
6x+2>16
6x>16-2
>14
$\frac{6x}{6}>\frac{14}{6}$
$x>\frac{7}{3}$
$\frac{6x+2}{4}<-4$
$\left(\frac{6x+2}{4}\right)\left(4\right)<\left(-4\right)\left(4\right)$
6x+2<-16
6x<-16-2
<-18
$\frac{6x}{6}<-\frac{18}{6}$
x<-3
Hence, x<-3 or $x>\frac{7}{3}$.

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