Q. 370 In the following exercises, solv... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 370 (page 732)

In the following exercises, solve each rational inequality and write the solution in interval notation.
$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$

Short Answer

Expert verified

Solution of rational inequality is $x 鈭� (- 鈭�, - 14] 鈭� (- 2, 1) .$

Step by step solution

Step 1. Given Information

Given that the rational inequality is $\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)} .$

Step 2. Critical points

On taking terms on left hand side,

$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)} \frac{5}{(x - 1)} - \frac{4}{(x + 2)} 鈮� 0 \frac{5}{(x - 1)} 脳 \frac{(x + 2)}{(x + 2)} - \frac{4}{(x + 2)} 脳 \frac{(x - 1)}{(x - 1)} 鈮� 0 \frac{5 (x + 2)}{(x - 1) (x + 2)} - \frac{4 (x - 1)}{(x - 1) (x + 2)} 鈮� 0 \frac{x + 14}{(x - 1) (x + 2)} 鈮� 0 (x + 14) = 0 x = - 14 (x - 1) (x + 2) = 0 x = 1, - 2$

At this critical point, the inequality is undefined. Thus, it cannot be a solution set.

Step 3. Testing of points

To test the points between critical points,

Step 4. Testing

It can be expressed as,

$At x = - 15, \frac{- 15 + 14}{(- 15 - 1) (- 15 + 2)} 鈮� 0 \frac{- 1}{208} 鈮� 0 True At x = - 5, \frac{- 5 + 14}{(- 5 - 1) (- 5 + 2)} 鈮� 0 \frac{9}{18} 鈮� 0 False At x = - 1, \frac{- 1 + 14}{(- 1 - 1) (- 1 + 2)} 鈮� 0 \frac{- 13}{2} 鈮� 0 True At x = 2, \frac{2 + 14}{(2 - 1) (2 + 2)} 鈮� 0 4 鈮� 0 False$

Thus, the solution set is $x 鈭� (- 鈭�, - 14] 鈭� (- 2, 1) .$

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91影视

In the following exercises, solve each rational inequality and write the solution in interval notation.
$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Critical points

Step 3. Testing of points

Step 4. Testing

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91影视

In the following exercises, solve each rational inequality and write the solution in interval notation.5(x-1)鈮�4(x+2)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Critical points

Step 3. Testing of points

Step 4. Testing

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each rational inequality and write the solution in interval notation.
$\frac{5}{(x - 1)} 鈮� \frac{4}{(x + 2)}$