Question

Determine all numbers such that $|x-6|=|6-x|$

Name: Problem 108, Chapter 4: Intermediate Algebra for College Students
Uploaded: 2023-02-19T03:55:44-08:00
Channel: Nick Johnson
Description: Determine all numbers such that |x-6|=|6-x|

   Determine all numbers such that $|x-6|=|6-x|$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 4, Problem 108

Instant Answer

Solved by Expert Nick Johnson

02/19/2023

Step 1

This means that the absolute values will be equal for any value of x, since the absolute value of a number and its opposite are always the same. Show more…

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Determine all numbers such that $|x-6|=|6-x|$

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Key Concepts

Absolute Value

The absolute value function measures the distance of a number from zero on the number line, always yielding a non-negative result. This concept is fundamental to understanding distances and magnitudes in various branches of mathematics.

Symmetry of the Absolute Value Function

A key property of the absolute value is its symmetry, where the absolute value of a number is the same as the absolute value of its negative. This means that |a| equals | -a| for any number a, which simplifies the analysis and manipulation of expressions involving absolute values.

Solving Absolute Value Equations

When dealing with equations that involve absolute value expressions, it is important to understand that such equations often require examining multiple cases or relying on inherent properties like symmetry. This general approach helps in systematically solving and understanding equations that might initially seem complex.

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