Solve the inequality.x2 + x - 12 ≥ 0

Question

asked Jun 1, 2023 18.8k views

1 Answer

Reteptilian · Answer 1 · 2023-06-05T20:40:46+0000

Solution:

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

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