# Solve the inequality. Express the answer using interval notation. |5x-2|<6

Solve the inequality. Express the answer using interval notation.
|5x-2|<6
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Step 1
To solve |5x-2|<6 , first remove the absolute value. The inequality of the form |x|<a can also be written as -a<x<a . Similarly the inequality |5x−2|<6 can be written as -6<5x-2<6 .
Step 2
To solve the inequality -6<5x-2 <6, first add 2 on all parts of the inequality and then divide the whole inequality by 5 and simplify.
-6<5x-2<6
-6+2<5x-2+2<6+2
-4<5x<8
$-\frac{4}{5}<\frac{5x}{5}<\frac{8}{5}$
$-\frac{4}{5}
Hence , the solution in interval notation is $\left(-\frac{4}{5},\frac{8}{5}\right)$.