Absolute Value Equations | Multi-Step & No Solution

Question:
Solve each equation, or state if there is no solution. Check all solutions. Part a: 2 times the absolute value of x plus 3, minus 5, equals 9. Part b: the absolute value of 4y minus 8, plus 6, equals 2. Part c: 3 times the absolute value of 2z minus 1, plus 4, equals 19.

Absolute Value Equations | Multi-Step & No Solution

This lesson teaches students how to solve absolute value equations by first isolating the absolute value expression, then splitting into two linear cases. Special attention is given to recognizing when an equation yields no solution because the isolated absolute value equals a negative number.

In this lesson, you will learn to:
• Isolate an absolute value expression using inverse operations
• Apply the definition of absolute value to split one equation into two linear equations
• Identify equations with no solution when the isolated absolute value equals a