Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Question
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Chapter A.6, Problem 86E
To determine

Find the interval on the real number line of the given using absolute value notation .

Expert Solution & Answer
Check Mark

Answer to Problem 86E

The absolute value notation of the given |x+1|≤4

Explanation of Solution

Given:

The figure

  Precalculus with Limits, Chapter A.6, Problem 86E , additional homework tip 1

Let consider the following figure.

  Precalculus with Limits, Chapter A.6, Problem 86E , additional homework tip 2

On analyzing the above figure, it is found that x is bounded by −5 and 3, that is, it cannot attain anyvalue beyond -5 and 3.

Therefore, it can be written as

  −5≤x≤3

Using the property that the solutions of |x|≤a are all values of x that lie between −a and a .

That is |x|≤a ifand only if −a≤x≤a .

Above expression can be written as

  −5≤x≤3

Adding 1 to both the sides, above expression can be written as

  −4≤x+1≤4

  |x+1|≤4

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Chapter A.6, Problem 85E
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Chapter A.6, Problem 87E

Chapter A Solutions

Precalculus with Limits

Ch. A.1 - Prob. 1ECh. A.1 - Prob. 2ECh. A.1 - Prob. 3ECh. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - Prob. 9ECh. A.1 - Prob. 10E
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