Answer:
The solution of the compound inequality is the interval [tex][-3,3][/tex]
Step-by-step explanation:
we have
[tex]3x+7\geq -2[/tex] -----> inequality A
[tex]8x-3\leq 21[/tex] ----> inequality B
Step 1
Solve the inequality A
[tex]3x\geq -2-7[/tex]
[tex]x\geq -9/3[/tex]
[tex]x\geq -3[/tex]
The solution of the inequality A is the interval---------> [-3,∞)
All real numbers greater than or equal to [tex]-3[/tex]
Step 2
Solve the inequality B
[tex]8x\leq 21+3[/tex]
[tex]x\leq 24/8[/tex]
[tex]x\leq 3[/tex]
The solution of the inequality B is the interval---------> (-∞,3]
All real numbers less than or equal to [tex]3[/tex]
Step 3
Find the solution of the compound inequality
[-3,∞) ∩ (-∞,3]=[-3,3]
