Answer:
Step-by-step explanation:
we have
[tex]18 > -5x+2 > -48[/tex]
This is a compound inequality
Remember that
A compound inequality i can divide in a system of two inequalities
so
[tex]18 > -5x+2[/tex] -----> inequality A
[tex]-5x+2 > -48[/tex] ---> inequality B
step 1
Solve the inequality A
[tex]18 > -5x+2[/tex]
Multiply by -1 both sides
[tex]-18< 5x-2[/tex]
[tex]-18+2< 5x[/tex]
[tex]-16< 5x[/tex]
Divide by 5 both sides
[tex]-3.2< x[/tex]
Rewrite
[tex]x > -3.2[/tex]
The solution of the inequality A is the interval ----> (-3.2,∞)
step 2
Solve the inequality B
[tex]-5x+2 > -48[/tex]
Multiply by -1 both sides
[tex]5x-2 < 48[/tex]
[tex]5x < 48+2[/tex]
[tex]5x < 50[/tex]
Divide by 5 both sides
[tex]x < 10[/tex]
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
