Chapter 7: Q. 375 (page 733)

Write the steps you would use to explain solving rational inequalities to your little brother.

Short Answer

Expert verified

Solution is $x \in (- \infty, - 4) \cup [- 1, \infty) .$

Step by step solution

Step 1. Given data

Consider the rational inequality is $R (x) = \frac{(x + 1)}{(x + 4)}$ .

Step 2. Critical points

Critical points are the points where rational expressions can be undefined or zero.

$(x + 1) = 0 x = - 1 (x + 4) = 0 x = - 4 (x + 1) = 0 x = - 1 (x - 4) = 0 x = 4$

Step 3. Number line

On dividing the number line using the critical points,

Step 4. Intervals

There are three intervals includes $(- \infty, - 4), (- 4, - 1), (- 1, \infty) .$

Take any value in the interval of $(- \infty, - 4) .$

$x = - 5 R (x) = \frac{- 5 + 1}{- 5 + 4} = 4 R (x) = + ve$

In the interval of $(- 4, - 1), take x = - 2,$

$R (x) = \frac{- 2 + 1}{- 2 + 4} = \frac{- 1}{2} = - ve$

In the interval of $(- 1, \infty), take x = 5, R (x) = \frac{5 + 1}{5 + 4} = \frac{2}{3} = + ve$

Step 5. Number line

The number line can be drawn as,

Step 6. Testing of values

To test the values, the number line sign can indicated.

$At x = - 1, R (x) = \frac{- 1 + 1}{- 1 + 4} = 0 At x = - 4, R (x) = \frac{- 4 + 1}{- 4 + 4} = \infty Thus, R (x) \geq 0 x \in (- \infty, - 4) \cup [- 1, \infty) .$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write the steps you would use to explain solving rational inequalities to your little brother.

Short Answer

Step by step solution

Step 1. Given data

Step 2. Critical points

Step 3. Number line

Step 4. Intervals

Step 5. Number line

Step 6. Testing of values

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.