Chapter 1.2

Solving absolute value equations

What You'll Learn

Convert absolute value expressions into piecewise functions with positive and negative cases
Identify critical points where absolute value functions change behavior by setting expressions equal to zero
Apply test values to determine which piece of the piecewise function applies in each region
Solve linear and quadratic equations resulting from removing absolute value notation
Verify solutions by checking if they fall within the appropriate regions on the number line

What You'll Practice

1

Solving equations with one absolute value expression equal to a linear function

2

Working with equations containing two different absolute value functions

3

Solving absolute value equations involving quadratic expressions

4

Checking solutions against regional constraints and rejecting invalid answers

Why This Matters

Solving absolute value equations builds your algebraic problem-solving skills and teaches you to handle piecewise scenarios that appear throughout higher math. You'll use these techniques in calculus, physics, and engineering courses where understanding behavior in different regions is critical.

Before You Start — Make Sure You Can:

Solving polynomial equationsSolving quadratic equations by factoringSolving quadratic equations by completing the squareAbsolute value functions

This Unit Includes

5 Video lessons
Practice exercises
Learning resources

Skills

Absolute Value
Piecewise Functions
Equation Solving
Number Line Analysis
Test Values
Quadratic Equations
Solution Verification
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MB Curriculum Aligned

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