Answer:
The graph in the attached figure ( is the third option)
Step-by-step explanation:
we have the compound inequality
[tex]-18> -5x+2\geq -48[/tex]
Divide the compound inequality in two inequalities
[tex]-18> -5x+2[/tex] -----> inequality A
[tex]-5x+2\geq -48[/tex] -----> inequality B
Step 1
Solve inequality A
[tex]-18> -5x+2[/tex]
[tex]-18-2> -5x[/tex]
[tex]-20> -5x[/tex]
Multiply by -1 both sides
[tex]20<5x[/tex]
[tex]4<x[/tex]
Rewrite
[tex]x > 4[/tex]
The solution of the inequality A is the interval ------>(4,∞)
Step 2
Solve the inequality B
[tex]-5x+2\geq -48[/tex]
[tex]-5x\geq -48-2[/tex]
[tex]-5x\geq -50[/tex]
Multiply by -1 both sides
[tex]5x\leq 50[/tex]
[tex]x\leq 10[/tex]
The solution of the inequality B is the interval -----> (-∞,10]
therefore
The solution of the compound inequality is
(4,∞) ∩ (-∞,10]=(4,10]
All real numbers greater than 4 (open circle) an less than or equal to 10 (close circle)
The solution in the attached figure
