# Section 2.7 – Nonlinear Inequalities

Section Details.
• Solving a nonlinear inequality and writing the answer in interval notation

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.

1. Solve $$-x^{2} + 9x \geq -22$$.

$$[-2,11]$$

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2. Solve $$\displaystyle{(x+5)^3(1-2x)^2 < 0}$$.

$$(-\infty,-5)$$

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3. Solve $$\displaystyle{9x^{2} + 6x + 1 > 0}$$.

$$\left(-\infty,-\dfrac{1}{3}\right)\cup\left(-\dfrac{1}{3},\infty\right)$$

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4. Solve $$\displaystyle{(x-100)^{2}\leq 0}$$.

$$\{100\}$$

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