Question

solve the compound inequality. 3w - 3 > 6 or 4w - 6 < - 10. graph the solution on the number line. if there is no solution, click on
o solution\.

Explanation:

Step1: Solve the first - inequality

Solve \(3w - 3>6\). Add 3 to both sides: \(3w-3 + 3>6 + 3\), which simplifies to \(3w>9\). Then divide both sides by 3: \(w > 3\).

Step2: Solve the second - inequality

Solve \(4w-6<-10\). Add 6 to both sides: \(4w-6 + 6<-10 + 6\), which simplifies to \(4w<-4\). Then divide both sides by 4: \(w<-1\).

Step3: Analyze the compound - inequality (or)

The compound inequality is \(3w - 3>6\) or \(4w-6<-10\). The solution set is the union of the solution sets of the two inequalities. So the solution is \(w < - 1\) or \(w>3\).

Answer:

The solution set is \(w < - 1\) or \(w>3\). On the number - line, an open circle at \(w=-1\) and shade to the left, and an open circle at \(w = 3\) and shade to the right.