Question

which graph represents the compound inequality below?
-10x - 9 ≤ -39 or 4x + 5 < -7

Explanation:

Step1: Solve the first inequality

$$\begin{align*} -10x - 9&\leq - 39\\ -10x&\leq -39 + 9\\ -10x&\leq - 30\\ x&\geq\frac{-30}{-10}\\ x&\geq3 \end{align*}$$

Step2: Solve the second inequality

$$\begin{align*} 4x+5&<-7\\ 4x&<-7 - 5\\ 4x&<-12\\ x&<\frac{-12}{4}\\ x&<-3 \end{align*}$$

Answer:

The solution of the compound inequality is \(x\geq3\) or \(x < - 3\). The graph will have a closed circle at \(x = 3\) and a ray going to the right (for \(x\geq3\)) and an open circle at \(x=-3\) and a ray going to the left (for \(x < - 3\)).