Question

1. solve and graph the inequality. show all steps.

• 3x + 5 < - 19

Explanation:

Step1: Subtract 5 from both sides

$$\begin{align*} -3x+5 - 5&<-19 - 5\\ -3x&<-24 \end{align*}$$

Step2: Divide both sides by -3 and reverse the inequality sign

$$\begin{align*} \frac{-3x}{-3}&>\frac{-24}{-3}\\ x&>8 \end{align*}$$

Step3: Graph the solution

On the number - line, draw an open circle at \(x = 8\) (because \(x>8\) and \(8\) is not included in the solution set) and shade the region to the right of \(8\).

Answer:

The solution of the inequality is \(x>8\). On the number - line, there is an open circle at \(8\) and the line is shaded to the right of \(8\).