Question

Solve the inequality.x^2 + 2x ≥ 24

Answer 1

`x\le-6\text{ or x}\ge4`

Explanation:

As a first step find the critical points of the inequality, factor the inequality in the form (x+a)(x+b):

`\begin{gathered} x^2+2x\ge24 \\ x^2+2x-24\ge0 \\ \text{ Factoring:} \\ (x-4)(x+6)=0 \\ x-4=0 \\ x=4 \\ \\ x+6=0 \\ x=-6 \end{gathered}`

Check intervals in between critical points;

`\begin{gathered} x\leq-6 \\ x\ge4 \\ \text{ Both work in the original inequality} \\ x\le-6\text{ or x}\ge4 \end{gathered}`