Warm Up 1. A=lw for w 2. 3. 4. -3v + 6 = 4v – 1 5. 3(2x – 4) = 4x + 4 Solve. 1. A=lw for w 2. 3. 4. -3v + 6 = 4v – 1 5. 3(2x – 4) = 4x + 4

Answers

Lesson 3.4 Solving Absolute Value Equations 1.1.3

Exploration Determine the solution for each equation. 4, -4 9, -9 No Solution

What did you notice? Summarize what you noticed from the previous solutions. When a variable is inside an absolute value, there are two solutions. When an absolute value is set equal to a negative number, there is no solution. (this is important to remember) Can you think of a situation where there would be one solution? When the absolute value is equal to zero.

**Need to isolate the absolute value expression** Steps for solving absolute value equations. **Need to isolate the absolute value expression** Undo addition or subtraction outside of absolute value. Undo multiplication or division outside of absolute value. Set expression inside absolute value equal to the given value and its opposite. Solve for variable using steps for solving equations. Distribute Combine Like Terms Move Variable to One Side Undo + or – Undo × or ÷

Examples Solving basic absolute value equations

Examples continued 1, 5 -24, 8

More Examples Solving absolute value equations when there are terms outside the symbols

Even More Examples 0, 8/3 -2, 6

Summary/Reflection Homework What is the difference between solving a regular equation and solving an equation where the variable is in an absolute value? How can you remember that absolute value equations have two solutions? Homework 3.4 worksheet