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Grade 11 Pre-Calculus Mathematics (30S)
Develop algebraic reasoning and number sense
1. Demonstrate an understanding of the absolute value of real numbers
1.2 Solving absolute value equations
Solving Absolute Value Equations
A step-by-step guide to solving absolute value equations, including the two-case method, extraneous solution checks, and worked examples.
What You'll Learn
An absolute value equation like x minus 4 in absolute value bars equals 9 must be split into two separate linear equations before solving.
Always isolate the absolute value expression on one side of the equation before splitting it into cases.
An equation where the absolute value expression equals a negative number has no solution, since absolute value is never negative.
Solutions must always be checked in the original equation, especially when the other side contains a variable, because extraneous solutions can appear.
Graphically, an absolute value equation asks where a V-shaped graph meets a horizontal or slanted line, which is why two solutions usually appear.
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:
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
MB Curriculum Aligned