Question

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.

$x^2\ge 9$

Short answer

The solution set of the given non-linear inequality is $\left(-\infty ,-3\right]\cup \left[3,\infty \right)$and the graph is

Step-by-step solution

Step 1. Consider the given inequality.

The given non-linear inequality is,

$x^2\ge 9\cdots \left(1\right)$

Step 2. Solve the inequality (1).

$x^2-9\ge 0$(Subtract from both sides).

$\left(x+3\right)\left(x-3\right)\ge 0\left[\because {a^2}^{}-b^2=\left(a+b\right)\left(a-b\right)\right]$

Therefore,$x\ge -3,x\ge 3$

Step 3. Write the obtained solution in the interval notation and graphed it.

The interval notation of the obtain solution $x\ge -3,x\ge 3$is, $\left(-\infty ,-3\right]\cup \left[3,\infty \right)$and graph is,