Solve. |6x+24|>4

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.
${\displaystyle \left|\frac{6x+2}{4}\right|>4}$
${\displaystyle \left(\frac{6x+2}{4}\right)>4}$...(1)
${\displaystyle -\left(\frac{6x+2}{4}\right)>4}$
${\displaystyle \left(\frac{6x+2}{4}\right)<-4}$...(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).
${\displaystyle \frac{6x+2}{4}>4}$
${\displaystyle \left(\frac{6x+2}{4}\right)\left(4\right)>\left(4\right)\left(4\right)}$
6x+2>16
6x>16-2
>14
${\displaystyle \frac{6x}{6}>\frac{14}{6}}$
${\displaystyle x>\frac{7}{3}}$
${\displaystyle \frac{6x+2}{4}<-4}$
${\displaystyle \left(\frac{6x+2}{4}\right)\left(4\right)<(-4)\left(4\right)}$
6x+2<-16
6x<-16-2
<-18
${\displaystyle \frac{6x}{6}<-\frac{18}{6}}$
x<-3
Hence, x<-3 or ${\displaystyle x>\frac{7}{3}}$.