Question

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

Answer 1

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