Question

use the number lines provided to graph the solution set for the inequalities.
things to keep in mind:
● did you solve for the variable?
● should the sign flip or stay the same?
● will you use a circle or a dot on the value?
● did you check your number line by testing out a value?
3x ≥ x - 8

Explanation:

Step1: Solve the inequality

$$\begin{align*} 3x&\geq x - 8\\ 3x-x&\geq x - 8-x\\ 2x&\geq - 8\\ x&\geq\frac{-8}{2}\\ x&\geq - 4 \end{align*}$$

Step2: Graph the solution on the number - line

Since \(x\geq - 4\), we use a closed dot (because the inequality includes equality, i.e., \(x = - 4\) is part of the solution) at \(-4\) and draw an arrow to the right (because \(x\) can be greater than \(-4\) as well).

Answer:

The solution of the inequality \(3x\geq x - 8\) is \(x\geq - 4\). On the number - line, place a closed dot at \(-4\) and draw an arrow to the right.