Question

Question 13 of 18Graph the solution to the following inequality on the number line.x² - 4x ≥ 12

Answer 1

Step 1

Given; Graph the solution to the following inequality on the number line.

x² - 4x ≥ 12

Step 2

`\begin{gathered} x^2-4x\ge \:12 \\ Rewrite\text{ in standard form} \\ x^2-4x-12\ge \:0 \\ Factor\text{ the inequality} \\ \left(x+2\right)\left(x-6\right)\ge \:0 \end{gathered}`
`\begin{gathered} Identify\text{ the intervals} \\ x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6 \end{gathered}`

Thus, the number line will look like

Answer; The solution to the inequality graphed on a number line is seen below

`x\le \:-2\quad \mathrm{or}\quad \:x\ge \:6`