# How do you solve the inequality -2x + 3 >7?

Dec 3, 2015

$x < - 2$

#### Explanation:

To solve a linear inequality, you can mostly behave the same way as you do when solving linear equations, with two important equations:

1. each time you multiply both sides with a negative number or if you divide both sides by a negative number, you need to "turn" the greater/less sign, so, transform $<$ into $>$ and vice versa
2. if you flip the sides of the equation, you also need to "turn" the greater/less sign.

With this knowledge, you can solve the inequality as follows:

$- 2 < + 3 > 7$

... add $- 3$ on both sides ...

$- 2 x > 4$

... divide by $- 2$ on both sides; don't forget to flip the inequality sign!

$x < - 2$

So, the solution is $x < - 2$.