Q. 56 Solve each inequality algebraica... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 56 (page 242)

Solve each inequality algebraically.
$(x - 3) (x + 2) < x^{2} + 3 x + 5$

Short Answer

Expert verified

Solution set and the interval is:

${x | x > - \frac{11}{4}} (- \frac{11}{4}, 鈭�)$

Step by step solution

Step 1. Change the inequality to equal to zero.

Change the inequality equal to zero to make it easier and then get the value of x

First arrange the inequality,

$\begin{aligned} (x 鈭� 3) (x + 2) < x^{2} + 3 x + 5 \\ x^{2} 鈭� x 鈭� 6 < x^{2} + 3 x + 5 \\ x^{2} 鈭� x 鈭� 6 鈭� x^{2} 鈭� 3 x 鈭� 5 < 0 \\ 鈭� 4 x 鈭� 11 < 0 \end{aligned}$

Make it equal to zero,

$- 4 x - 11 = 0 4 x + 11 = 0 x = - \frac{11}{4}$

Step 2. Form the intervals

From the obtained values of x, we can form the interval,

So the interval we have is:

$(- 鈭�, - \frac{11}{4}) 鈭� (- \frac{11}{4}, 鈭�)$

Step 3. Form the table

Since, $f (x) < 0$ , so is negative.

check a number in each interval and evaluate the function to see whether it is satisfying the function.

Interval	Number chosen	Resultant
$(- 鈭�, - \frac{11}{4})$	-3	$1 < 0$
$(- \frac{11}{4}, 鈭�)$	5	$- 31 < 0$

Step 4. Solution set and interval

Since, only $- 31 < 0$ satisfy $f$ . Thus,

role="math" localid="1646211136842" ${x | x > - \frac{11}{4}} (- \frac{11}{4}, 鈭�)$

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91影视

Solve each inequality algebraically.
$(x - 3) (x + 2) < x^{2} + 3 x + 5$

Short Answer

Step by step solution

Step 1. Change the inequality to equal to zero.

Step 2. Form the intervals

Step 3. Form the table

Step 4. Solution set and interval

One App. One Place for Learning.

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91影视

Solve each inequality algebraically.(x-3)(x+2)<x2+3x+5

Short Answer

Step by step solution

Step 1. Change the inequality to equal to zero.

Step 2. Form the intervals

Step 3. Form the table

Step 4. Solution set and interval

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Pure Maths

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each inequality algebraically.
$(x - 3) (x + 2) < x^{2} + 3 x + 5$