Question

solve the compound inequality.
4x + 3 < -9 or 2x + 3 ≥ 15
graph the solution on the number line.

Explanation:

Step1: Solve \(4x + 3<-9\)

Subtract \(3\) from both sides:
\(4x+3 - 3<-9 - 3\)
\(4x<-12\)
Divide both sides by \(4\):
\(x < - 3\)

Step2: Solve \(2x + 3\geq15\)

Subtract \(3\) from both sides:
\(2x+3 - 3\geq15 - 3\)
\(2x\geq12\)
Divide both sides by \(2\):
\(x\geq6\)

Answer:

The solution of the compound inequality \(4x + 3<-9\) or \(2x + 3\geq15\) is \(x < - 3\) or \(x\geq6\). On the number - line, we have an open circle at \(x = - 3\) and shade to the left of \(x=-3\), and a closed circle at \(x = 6\) and shade to the right of \(x = 6\).