6-5A Solving Absolute Value Equations Get branching technique from Teresa regarding absolute value problems! Algebra 1 Glencoe McGraw-Hill Linda Stamper

Absolute value is the distance a number is from zero Absolute value is the distance a number is from zero. Distance is never negative!

• • An absolute value equation is an equation of the form The value of c cannot be less than zero because absolute value always indicates a number that is NOT negative. To solve absolute value equations, write the two related linear equations and then solve them. There are two values of x that have an absolute value of 8. • • -8 8 These are the two related linear equations! The equations are solved because the variable is isolated!

How to Solve Absolute Value Equations. 1. Write the absolute value equation. 2. Isolate the absolute value on one side of the equal sign. 3. Write the two related linear equations. Note: These equations will NOT have absolute value bars! 4. Solve each equation independently. no solution An absolute value equation can have two solutions, one solution or no solution.

Solve. Then graph the solution. Example 1 Example 2 Example 3 Example 4

• • Example 1 Solve. Then graph the solution. 24, -24 no solution 

• • • • or or Solve. Then graph the solution. Example 4 Example 3 -4, 12 • • • • -4 12 5

Solve. Example 5 Example 6 Example 7 Example 8 Example 9 Example 10

You can NOT distribute through absolute value bars! Solve. Example 6 Example 5 No solution The absolute value of a number is never negative! or You can NOT distribute through absolute value bars! -4, 1 Note: Before you can write the two related linear equations you must isolate the absolute value!

Solve. Example 8 Example 7 or or 3, 4 -6, -4

or Solve. Example 10 Example 9 No solution The absolute value of a number is never negative! or -2, 10

Example 10 Check by substitution.

Homework 6-A10 Pages 325–327 # 7–18 (do not graph), 53–58.