Warm Up Warm Up

1. A=lw for w1. A=lw for w

2. 2.

3. 3.

Solve.

4. -3v + 6 = 4v – 14. -3v + 6 = 4v – 1

5. 3(2x – 4) = 4x + 45. 3(2x – 4) = 4x + 49

32 for C5

F C

1 for h

2A bh

AnswersAnswers1.

52. ( 32)

92

3.

4. 1

5. 8

Aw

l

C F

Ah

bv

x

Lesson 3.4 Solving Absolute Lesson 3.4 Solving Absolute Value EquationsValue Equations

1.1.31.1.3

ExplorationExploration

Determine the solution for each equation.Determine the solution for each equation.

6

9

4

c

n

x 4,4, -44

9,9, -99

No SolutionNo Solution

What did you notice?What did you notice?

Summarize what you noticed from the Summarize what you noticed from the previous solutions.previous solutions.

When the absolute value is equal to zero.When the absolute value is equal to zero.

When a variable is inside an absolute value, there When a variable is inside an absolute value, there are two solutions.are two solutions. When an absolute value is set equal to a negative When an absolute value is set equal to a negative number, there is no solution. (this is important to number, there is no solution. (this is important to remember)remember) Can you think of a situation where there would be Can you think of a situation where there would be one solution?one solution?

Steps for solving Steps for solving absolute value absolute value equations.equations.

**Need to isolate the absolute **Need to isolate the absolute value expression**value expression**

1)1) Undo addition or Undo addition or subtraction outside of subtraction outside of absolute value.absolute value.

2)2) Undo multiplication or Undo multiplication or division outside of absolute division outside of absolute value.value.

3)3) Set expression inside Set expression inside absolute value equal to the absolute value equal to the given value and its opposite.given value and its opposite.

4)4) Solve for variable using Solve for variable using steps for solving equations.steps for solving equations.

1.1. DistributeDistribute

2.2. Combine Like TermsCombine Like Terms

3.3. Move Variable to One SideMove Variable to One Side

4.4. Undo + or –Undo + or –

5.5. Undo Undo × or ÷× or ÷

ExamplesExamples

Solving basic Solving basic absolute value absolute value equationsequations 5 12 and 5 12x x

1. 5 12x

5 12 and 5 12x x 5 5 55

17x 7x

Examples continuedExamples continued

-24, 8-24, 8

13. 4 8

2x

2. 2 6 4x

1, 51, 5

More ExamplesMore Examples

Solving Solving absolute value absolute value equations equations when there are when there are terms outside terms outside the symbolsthe symbols

1. 1 4 12x

1 4 12x 4 4

1 16x 1 16 and 1 16x x 1 16 and 1 16x x 1 1 1 1

15 and 17x x

Even More ExamplesEven More Examples

-2, 6-2, 6

6. 3 2 4 6 18x

0, 8/30, 8/3

5. 3 4 6 10x

Summary/ReflectionSummary/Reflection

What is the difference between solving a What is the difference between solving a regular equation and solving an equation regular equation and solving an equation where the variable is in an absolute value?where the variable is in an absolute value?

How can you remember that absolute value How can you remember that absolute value equations have two solutions?equations have two solutions?

HomeworkHomework3.4 worksheet3.4 worksheet