# How do you solve the inequality: -5(13x + 3) < - 2(13x - 3)?

Aug 30, 2015

$x \in \left(- \frac{7}{13} , + \infty\right)$

#### Explanation:

Start by dividing both sides of the inequality by $\left(- 1\right)$ - do not forget to change the sign of the inequality when you do this

$\frac{- 5 \left(13 x + 3\right)}{\left(- 1\right)} > \frac{- 2 \left(13 x - 3\right)}{\left(- 1\right)}$

$5 \left(13 x + 3\right) > 2 \left(13 x - 3\right)$

Next, use the distributive property of multiplication to expand the two parantheses

$5 \cdot 13 x + 5 \cdot 3 > 2 \cdot 13 x + 2 \cdot \left(- 3\right)$

$65 x + 15 > 26 x - 6$

Rearrange to get the $x$-term on one side of the inequality

$65 x - 26 x > - 6 - 15$

$39 x > - 21 \implies x > - \frac{21}{39} = - \frac{7}{13}$

This means that your inequality will be true for any value of $x$ that is greater than $- \frac{7}{13}$. The solution set for this inequality will be $x \in \left(- \frac{7}{13} , + \infty\right)$.