/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 Solve each absolute value inequa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 60

Solve each absolute value inequality. $$|x+3| \leq 4$$

Short Answer

Expert verified
The solution to the inequality |x+3| 鈮� 4 is -7 鈮� x 鈮� 1.

Step by step solution

01

Set up equivalent inequalities.

Since the absolute value of an expression is either equal to the expression itself or its opposite when it鈥檚 less than or equal to a certain number, we have to start by setting up two equivalent inequalities:\n\[x + 3 \leq 4\]\nand\n\[-(x + 3) \leq 4\]
02

Simplify the inequalities.

We need to solve for \(x\) in each of the two inequalities from Step 1. Simplification by isolating \(x\) gives:\n\[x \leq 4 - 3\]\nfor the first inequality and\n\[-x - 3 \leq 4\]\nfor the second one. This further simplifies to:\n\[x \leq 1\]\nand\n\[-x \leq 4 + 3\]\nor\n\[-x \leq 7\] respectively.
03

Solve the second inequality.

The negative sign attached to \(x\) in the second inequality \[-x \leq 7\] means that \(x\) is greater than or equal to -7. So, we can rewrite the second inequality as\n\[x \geq -7\].
04

Combine the solutions.

Our result indicates that \(x\) has to be less than or equal to 1 AND more than or equal to -7.\nFormulating this, our solution is: \[-7 \leq x \leq 1\]. Meaning any value between -7 and 1 inclusive is a solution to the given inequality.

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

Most popular questions from this chapter

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?

Will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -3 and ending with 3

What does it mean to solve a formula for a variable?

$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'll win the contest if I can complete the crossword puzzle in 20 minutes plus or minus 5 minutes, so my winning time, \(x,\) is modeled by \(|x-20| \leq 5\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.