Question

Solve the inequality.x2 + x - 12 ≥ 0

Answer 1

Given the inequality:

`x^2+x-12\ge0`

Step 1: Factorize the left-hand side of the inequality.

Thus,

`\begin{gathered} x^2+x-12\ge0 \\ x^2-3x+4x-12\ge0 \\ x(x-3)+4(x-3)\ge0 \\ (x+4)(x-3)\ge0 \end{gathered}`

Step 2: Identify the intervals.

`\begin{gathered} x+4\ge0 \\ \Rightarrow x\le\: -4 \\ x-3\ge0 \\ \Rightarrow\: x\ge\: 3 \end{gathered}`

Hence, the solution to the inequality is

`\: x\le\: -4\text{ or }x\ge\: 3`