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Q. 2

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Found in: Page 241

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Solve the inequality ${x}^{2}-5x\le 24$. Graph the solution set.

The solution set of given inequality is $\left[-3,8\right]$ and its graph is

See the step by step solution

## Step 1. Using mathematical operations, solve the inequality.

First replace inequality symbol with an equality symbol.

${x}^{2}-5x=24\phantom{\rule{0ex}{0ex}}{x}^{2}-5x-24=0$

Now factorize the quadratic equation.

Find two terms whose sum is -5x and multiplication $-24{x}^{2}$.

${x}^{2}-8x+3x-24=0\phantom{\rule{0ex}{0ex}}x\left(x-8\right)+3\left(x-8\right)=0$

Taking common terms out.

$\left(x-8\right)\left(x+3\right)=0$ gives

$x-8=0orx+3=0\phantom{\rule{0ex}{0ex}}x=8orx=-3$

As the inequality was not strict in question, so the solution set of ${x}^{2}-5x\le 24$ will be $-3\le x\le 8$ or $\left[-3,8\right]$.

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