Option A:
x ≥ 14 AND x > 21
Solution:
Given compound inequality:
[tex]9 x+6 \geq 132 \quad A N D \quad-7 x+19<-128[/tex]
Let us take first inequality.
[tex]9 x+6 \geq 132[/tex]
Subtract 6 on both sides.
[tex]9 x+6-6 \geq 132-6[/tex]
[tex]9 x\geq 126[/tex]
Divide by 9 on both sides, we get
x ≥ 14
Let us take the second inequality.
[tex]-7 x+19<-128[/tex]
Subtract 19 on both sides.
[tex]-7 x+19-19<-128-19[/tex]
[tex]-7 x<-147[/tex]
Divide by –7 on both sides, we get
x > 21
x ≥ 14 AND x > 21
Option A is the correct answer.
Hence the solution is x ≥ 14 AND x > 21.
