# How do you solve and graph the compound inequality 3x>=5 or -5/8x-6>1 ?

Jun 10, 2015

It is the union of the two solution sets.

#### Explanation:

3x>=5 or −58x−6>1
$x \ge \frac{5}{3} \mathmr{and} 58 x < - 7$
$x \ge \frac{5}{3} \mathmr{and} x < - \frac{7}{58}$
You will have two semi-plane. The "or" operator means that you have to take the union of the two solution set.

graph{x>=5/3 [-10, 10, -5, 5]}

graph{x<-7/58 [-10, 10, -5, 5]}

Jun 10, 2015

Solve and graph system
(1) 3x >= 5
(2) -5x/8 - 6 > 1

#### Explanation:

(1) -> $3 x \ge 5 - \to x \ge \frac{5}{3}$

(2) -> $5 \frac{x}{8} < - 7 \to 5 x < - 56 \to x < - \frac{56}{5}$
Graph:

=========|-56/5 -----------------|0-----|5/3=============

NOTE. The end (critical) point (5/3) is included in the solution set.