/*! 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 53 Explain why the equation $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 53

Explain why the equation $$ |8 x-3|=-2 $$ has no solutions.

Short Answer

Expert verified
The equation \(|8x - 3| = -2\) has no solutions because the absolute value of an expression, which represents the distance of a number from zero on the number line, can never equal a negative number. In this case, the right side of the equation is -2, a negative number, making the equation impossible.

Step by step solution

01

Understand the properties of absolute values

An absolute value represents the distance of a number from zero on the number line. It is always a non-negative number, i.e., greater than or equal to zero.
02

Analyze the given equation

We have the equation \(|8x - 3| = -2\). The left side is the absolute value of an expression while the right side is a negative number.
03

Determine if the equation is valid

Since the left side of the equation is an absolute value, it can never be a negative number. However, the right side of the equation is -2, which is a negative number. This means that this equation is impossible and has no solutions.
04

Conclusion

The equation \(|8x - 3| = -2\) has no solutions because the absolute value of an expression can never equal a negative number.

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

The intersection of two sets of numbers consists of all numbers that are in both sets. If \(A\) and \(B\) are sets, then their intersection is denoted by \(A \cap B .\) In Exercises \(31-40,\) write each intersection as a single interval. $$ [-2,8] \cap(-1,4) $$

Simplify the given expression as much as possible. $$ \frac{x-3}{4}-\frac{5}{y+2} $$

Give an example of two irrational numbers whose product is a rational number.

In Exercises \(7-16,\) write each union as a single interval. $$ (-\infty,-10] \cup(-\infty,-8] $$

Simplify the given expression as much as possible. $$ \frac{3}{4}+\frac{6}{7} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.