Question

Which of the following is the correct graph of the solution to the inequality-18>-5x+2>-48

Answer 1

Answer:

Step-by-step explanation:

we have

$18 > -5x+2 > -48$

This is a compound inequality

Remember that

A compound inequality i can divide in a system of two inequalities

so

$18 > -5x+2$ -----> inequality A

$-5x+2 > -48$ ---> inequality B

step 1

Solve the inequality A

$18 > -5x+2$

Multiply by -1 both sides

$-18< 5x-2$

$-18+2< 5x$

$-16< 5x$

Divide by 5 both sides

$-3.2< x$

Rewrite

$x > -3.2$

The solution of the inequality A is the interval ----> (-3.2,∞)

step 2

Solve the inequality B

$-5x+2 > -48$

Multiply by -1 both sides

$5x-2 < 48$

$5x < 48+2$

$5x < 50$

Divide by 5 both sides

$x < 10$

The solution of the inequality B is the interval ----> (-∞, 10)

step 3

Find the solution of the compound inequality

(-3.2,∞) ∩ (-∞, 10)=(-3.2,10)

All real numbers greater than -3.2 and less than 10

The graph in the attached figure