# How do you solve and graph the compound inequality 3x > 3 or 5x < 2x - 3 ?

Jul 23, 2018

$\text{ }$
Solution:

color(red)[(x>1) or (x < -1)

Interval Notation:

color(red)((-oo, -1) uu (1,oo)

#### Explanation:

$\text{ }$
We are given the inequality expression:

color(blue)(3x > 3 or 5x < 2x - 3

Since the color(red)(Or operator is used, we will use color(red)(uu in our final solution.

Solve the inequality expressions separately:

color(blue)(3x>3

Divide both the sides of the inequity by color(red)(3

$\frac{3 x}{3} > \frac{3}{3}$

$\frac{\cancel{3} x}{\cancel{3}} > \frac{3}{3}$

color(blue)(x > 1 ... Res.1

color(blue)(5x < 2x - 3

Subtract color(red)(2x from both sides of the inequality.

$5 x - 2 x < 2 x - 3 - 2 x$

$5 x - 2 x < \cancel{2 x} - 3 - \cancel{2 x}$

$3 x < - 3$

Divide both sides of the inequality by color(red)(3

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

$\frac{\cancel{3} x}{\cancel{3}} < - \frac{3}{3}$

color(blue)(x<-1 ... Res.2

Hence, the final solutions:

color(red)[(x>1) or (x < -1)

Interval Notation:

color(red)((-oo, -1) uu (1,oo)

Represent the solution on a graph:

Dotted Lines on the graph indicate values that are NOT part of the Solution Set.

Hope it helps.