# How do you solve the inequality | 3x - 4 | > | 2x + 1 |?

$\textcolor{red}{\left(- \infty , \frac{3}{5}\right] \cup \left[5 , + \infty\right)}$

#### Explanation:

Given $\left\mid 3 x - 4 \right\mid > \left\mid 2 x + 1 \right\mid$

$+ \left(3 x - 4\right) > 2 x + 1$

$+ \left(3 x - 4 + 4 - 2 x\right) > 2 x + 1 + 4 - 2 x$

$\textcolor{red}{x > 5}$

$- \left(3 x - 4\right) > 2 x + 1$

$- 3 x + 4 > 2 x + 1$

$- 3 x - 2 x + 4 - 4 > 2 x - 2 x + 1 - 4$

$- 5 x$>$- 3$

Dividing by $- 5$ will change $>$ to $<$

$\frac{- 5 x}{- 5}$<$\frac{- 3}{- 5}$

$\textcolor{red}{x}$$\textcolor{red}{<}$$\textcolor{red}{\frac{3}{5}}$

God bless....I hope the explanation is useful.