Question

solve the compound inequality.
4x - 2 > -2 or 2x - 2 < -10
graph the solution on the number line.

Explanation:

Step1: Solve \(4x - 2>-2\)

Add \(2\) to both sides: \(4x-2 + 2>-2 + 2\), so \(4x>0\).
Divide both sides by \(4\): \(x > 0\).

Step2: Solve \(2x-2<-10\)

Add \(2\) to both sides: \(2x-2 + 2<-10 + 2\), so \(2x<-8\).
Divide both sides by \(2\): \(x<-4\).

Answer:

The solution of the compound inequality \(4x - 2>-2\) or \(2x - 2<-10\) is \(x < - 4\) or \(x>0\). On the number - line, we have an open circle at \(x = - 4\) and shade to the left of \(x=-4\), and an open circle at \(x = 0\) and shade to the right of \(x = 0\).