Chapter 4: Q. 2 (page 241)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Using mathematical operations, solve the inequality.

First replace inequality symbol with an equality symbol.

$x^{2} - 5 x = 24 x^{2} - 5 x - 24 = 0$

Now factorize the quadratic equation.

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

$x^{2} - 8 x + 3 x - 24 = 0 x (x - 8) + 3 (x - 8) = 0$

Taking common terms out.

$(x - 8) (x + 3) = 0$ gives

$x - 8 = 0 o r x + 3 = 0 x = 8 o r x = - 3$

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

Step 2. The graph to show the solution set of x2-5x≤24 is as follows.

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

Short Answer

Step by step solution

Step 1. Using mathematical operations, solve the inequality.

Step 2. The graph to show the solution set of x2-5x≤24 is as follows.

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Solve the inequality x2-5x≤24. Graph the solution set.

Short Answer

Step by step solution

Step 1. Using mathematical operations, solve the inequality.

Step 2. The graph to show the solution set of x2-5x≤24 is as follows.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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