# How do you solve and graph (3x - 5) / 2 < 2x + 2?

Aug 28, 2015

$x > - 9$

#### Explanation:

Your goal here is to isolate $x$ on one side of the inequality. Start by multiplying the right-hand side of the inequality by $1 = \frac{2}{2}$

$\frac{3 x - 5}{2} < \left(2 x + 2\right) \cdot \frac{2}{2}$

This is equivalent to

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

$3 x - 5 < 4 x + 4$

Now move $- 5$ and $4 x$ on the other sides of the inequality - don't forget to change their signs when you do that!

$3 x - 4 x < 4 + 5$

$- x < 9$

$x > - 9$

This means that your inequality will be satisfied by any value of $x$ that is bigger than $- 9$. The solution set will be $x \in \left(- 9 , + \infty\right)$.

You can graph this by drawing a dashed vertical line at $x = - 9$. Since you need the values of $x$ that are bigger than $- 9$, shade the area to the right of the dashed vertical line.

graph{x > -9 [-18.02, 18.03, -9.01, 9.01]}