# How do you solve  -5x+7 > -3?

Apr 3, 2018

Solution of the inequality is $x < 2$

#### Explanation:

Given:

The inequality $- 5 x + 7 > - 3$

Subtract $7$ from both sides of the inequality

$\Rightarrow - 5 x + 7 - 7 > - 3 - 7$

$\Rightarrow - 5 x + \cancel{7} - \cancel{7} > - 3 - 7$

$\Rightarrow - 5 x > - 10$

Multiply both the sides by $\left(- 1\right)$

Please remember to reverse the inequality

$\Rightarrow \left(- 5 x\right) \left(- 1\right) < \left(- 10\right) \left(- 1\right)$

$\Rightarrow 5 x < 10$

Divide both sides by 5

$\Rightarrow \frac{5 x}{5} < \frac{10}{5}$

$\Rightarrow \frac{\cancel{5} x}{\cancel{5}} < {\cancel{10}}^{\textcolor{red}{2}} / \cancel{5}$

$\Rightarrow x < 2$

Hence $x < 2$ is the required solution.

Verify this solution with the graph below: