Question

consider the following inequality.

8 - 4x ≥ 20

solve the inequality for x.

graph the solution.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

change endpoint solidity

change arrow direction

Explanation:

Step1: Subtract 8 from both sides

$$\begin{align*} 8-4x - 8&\geq20 - 8\\ -4x&\geq12 \end{align*}$$

Step2: Divide both sides by -4 and reverse the inequality sign

$$\begin{align*} \frac{-4x}{-4}&\leq\frac{12}{-4}\\ x&\leq - 3 \end{align*}$$

Answer:

The solution of the inequality \(8 - 4x\geq20\) is \(x\leq - 3\). On the number - line, we have a solid circle at \(x = - 3\) (since the inequality includes equality, i.e., \(\geq\) after manipulation becomes \(\leq\) and the original inequality \(8-4x\geq20\) is equivalent to \(x\leq - 3\)) and the arrow points to the left (towards the negative infinity).