Solving Multi-Step Absolute-Value Equations
Solve multi-step absolute-value equations in Grade 9 algebra by isolating the absolute value expression first, then splitting into two equations representing positive and negative cases.
Key Concepts
New Concept The absolute value of a number is the distance the number is from $0$ on a number line. What’s next Next, you’ll learn to isolate the absolute value expression and solve the two resulting linear equations to find the solutions.
Common Questions
What are the steps to solve a multi-step absolute value equation?
First isolate the absolute value expression on one side using inverse operations. Then split into two equations: one setting the expression inside equal to the positive value, and one equal to the negative value. Solve both and check solutions.
How do you solve 2|x - 3| + 4 = 14?
Step 1: Subtract 4 from both sides: 2|x - 3| = 10. Step 2: Divide by 2: |x - 3| = 5. Step 3: Split: x - 3 = 5 or x - 3 = -5. Solving gives x = 8 or x = -2.
When does an absolute value equation have no solution?
An absolute value equation has no solution when, after isolating the absolute value, the right side is negative. For example, |x + 1| = -3 has no solution because absolute value is always non-negative.