Solve the equation. |x-3|=2

Name: Problem 9, Chapter 1: College Algebra
Uploaded: 2020-08-06T20:06:46-08:00
Duration: 37 s
Channel: Ankit Gupta
Description: Solve the equation. |x-3|=2

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Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, always resulting in a non-negative value. It is formally defined as being equal to the number itself if the number is non-negative, or the opposite of the number if it is negative.

Solving Absolute Value Equations

When solving equations that include absolute value expressions, one typically splits the problem into two separate cases based on the definition of absolute value. This involves setting the internal expression equal to both the positive and negative of the number on the other side of the equation, assuming that number is non-negative.

Piecewise Definition of Absolute Value

The concept of the absolute value is inherently piecewise, meaning it is defined by different rules depending on whether the input is non-negative or negative. This understanding is essential when solving equations with absolute values, as it requires considering each case individually to obtain all possible solutions.

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