Question

Solve the equations. $|2 a-3|=|a+2|$

   Solve the equations. 
$|2 a-3|=|a+2|$

College Algebra Essentials

College Algebra Essentials

Julie Miller 1st Edition

Chapter 1, Problem 26

Instant Answer

Solved by Expert Melissa Barry

08/08/2021

Step 1

This gives us two equations to solve: \[2a - 3 = a + 2\] and \[2a - 3 = -(a + 2)\] Show more…

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Solve the equations. $|2 a-3|=|a+2|$

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Key Concepts

Absolute Value

The absolute value of a number or expression represents its distance from zero, regardless of its sign. This fundamental concept is used to measure magnitudes without considering the direction on the number line.

Solving Absolute Value Equations

When solving equations that involve absolute values, one typically sets up multiple cases to consider both the positive and negative possibilities of the expressions inside the absolute values. This ensures that all potential solutions are explored.

Case Analysis

Case analysis is an essential strategy in solving absolute value equations, where the equation is split into different scenarios based on the possible signs of the expressions within the absolute values. Each case leads to a separate equation that must be solved to find all valid solutions.

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