# How do you solve -2/3x-4 < -8x-2?

Apr 29, 2018

$x < \frac{3}{11}$

#### Explanation:

$- \frac{2}{3} x - 4 < - 8 x - 2$

First, add $4$ to both sides of the inequality:
$- \frac{2}{3} x - 4 \quad \textcolor{red}{+ \quad 4} < - 8 x - 2 \quad \textcolor{red}{+ \quad 4}$

$- \frac{2}{3} x < - 8 x + 2$

Add $8 x$ to both sides of the inequality:
$- \frac{2}{3} x \quad \textcolor{red}{+ \quad 8 x} < - 8 x + 2 \quad \textcolor{red}{+ \quad 8 x}$

$7 \frac{1}{3} x < 2$

$\frac{22}{3} x < 2$

Multiply both sides by $3$:
$\frac{22}{3} x \textcolor{red}{\cdot \quad 3} < 2 \textcolor{red}{\cdot \quad 3}$

$\frac{22}{\cancel{3}} x \cancel{\textcolor{red}{\cdot \quad 3}} < 6$

$22 x < 6$

$x < \frac{6}{22}$

Divide numerator and denominator by $2$:
$x < \frac{6}{22} \textcolor{red}{\div \frac{2}{2}}$

$x < \frac{3}{11}$

Hope this helps!