Q. 57 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. 57 (page 242)

Solve each inequality algebraically.
$6 x - 5 < \frac{6}{x}$

Short Answer

Expert verified

Solution set and the interval is:
${x | - \frac{2}{3} < x < \frac{3}{2}} (- \frac{2}{3}, \frac{3}{2})$

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,

$6 x - 5 < \frac{6}{x} 6 x - 5 - \frac{6}{x} < 0 6 x^{2} - 5 x - 6 < 0$ Make it equal to zero,

$6 x^{2} - 5 x - 6 = 0 (3 x + 2) (2 x - 3) = 0 3 x + 2 = 0; 2 x - 3 = 0 x = - \frac{2}{3}; x = \frac{3}{2}$

Step 2. Form the intervals

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

So the interval we have is:

$(- 鈭�, - \frac{2}{3}) 鈭� (- \frac{2}{3}, \frac{3}{2}) 鈭� (\frac{3}{2}, 鈭�)$

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
$(- 鈭�, - \frac{2}{3})$	$- 2$	$28 < 0$
$(- \frac{2}{3}, \frac{3}{2})$	$0$	$- 6 < 0$
$(\frac{3}{2}, 鈭�)$	$2$	$8 < 0$

Step 4. Solution set and interval

Since,

$- 6 < 0$ satisfy $f$ . Thus,

role="math" localid="1646201857095" ${x | - \frac{2}{3} < x < \frac{3}{2}} (- \frac{2}{3}, \frac{3}{2})$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve each inequality algebraically.
$6 x - 5 < \frac{6}{x}$

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

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Calculus

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Solve each inequality algebraically. 6x-5<6x

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

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Calculus

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each inequality algebraically.
$6 x - 5 < \frac{6}{x}$