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Copy of Day 3 Absolute Value Equations.notebook November 13, 2019

Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

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Page 1: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Page 2: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Absolute Value Equations

Ex(1)  Solve the following.

|x| = 8

Absolute Value Equation: An equation that includes the absolute value of an expression involving a variable.

To solve absolute value equations, we must consider both cases of the definition of absolute value.

Page 3: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Steps for solving Absolute Value Equations:

1. Write down the absolute value function as a piecewise function.

> Write the equation in both the positive and negative forms.

> Determine the invariant points (x­intercepts) to help write the domain for each equation.

2. Solve for the variable in each.3. Verify the solution.  You MUST check for extraneous 

roots!!!

Page 4: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Ex(2) Solve the following equation

|x + 2| = 7

Let's see what the graph of this looks like.

Use DESMOS

Page 5: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Ex(3) Solve the following equation

|2x ­ 5| = 5 ­ 3x

Page 6: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Ex(4) Solve the following equation

|2x ­ 2| + 3 = 1

Page 7: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Ex(5) Solve the following equation

|x2 ­ 2x| = 1

Page 8: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Ex(6)  Solve the following equation

|x ­ 10| = x2 ­ 10x

Page 9: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019

Complete the following:

pg. 389­90, # 4 ­ 6, 10, 15, 22

Page 10: Copy of Day 3 - Absolute Value Equations.notebook€¦ · Copy of Day 3 Absolute Value Equations.notebook November 13, 2019 Steps for solving Absolute Value Equations: 1. Write down

Copy of Day 3 ­ Absolute Value Equations.notebook November 13, 2019