Solving Absolute Value Equations

Solving Absolute Value Equations

by Sahel Otoom

Multiple Choice

Before (Warm Up)

What is the vertex of $$f\left(x\right)=6\left|x-1\right|-2$$  ?

• (6,-1)

• (-1,-2)

• (1,-2)

• (1,2)

​Objectives

​ - Identifying Absolute - value equations.

​

- Solve equations in one variable that contain absolute-value expressions.

​Vocabulary

​Absolute Value Expressions.

​

​

​

​

Absolute Value Equation.

​Absolute value equations are equations where the variable is within an absolute value operator,

like |x-5|=9. 

Multiple Choice

An absolute value equation is

• an equation that contains an absolute value expression

• always going to have two solutions

• always going to have one solution

• impossible to solve

Multiple Choice

Solve for X

|X|=7

• X= 7

• X= -7

• X= 7 and X= -7

• No Solution

Multiple Choice

Solve for X

|X| = -3

• X= 3 and X= -3

• X= 3

• X= -3

• No Solution

Multiple Choice

What would be the correct setup for solving for X?

|X+3| = 5

• X+3= 5 and X+3= -5

• X+3= 5 ad X-3= 5

• X+3= -5 and X-3 = -5

• X+3= 5 and -X-3= -5

Multiple Choice

( EMSAT) Solve for x

-6|-2x - 7| = -18

• {-5,-2}

• {5,-2}

• {-5,2}

• {5,2}

Multiple Choice

solve for z.

|3z|+1=10

• {-3,3}

• {3,4}

• {-3,6}

• {-2,3}

Multiple Choice

Solve

∣ 2x + 9 ∣ = 15

• { -6,3}

• { -12,6}

• {3}

• { -12,3}

Multiple Choice

Solve

2| x – 3 |+8= 8

• 3

• -3

• {-3, 3}

• no solution

Multiple Select

An absolute value equation can have which numbers of solutions?

(select all that apply)

• No Solution

• 1 Solution

• 2 Solutions

• 4 Solutions

• 5Solutions

Multiple Choice

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

• No solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

• No solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

The graphs here represent the two sides of an absolute value equation. How many solutions does the equation have?

• No solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

For an absolute value equation to have ONE solution, which of the following should be true?

• |__| = +

• |__| = -

• |__| = 0

Multiple Choice

For an absolute value equation to have TWO solution, which of the following should be true?

• |__| = +

• |__| = -

• |__| = 0

Multiple Choice

For an absolute value equation to have NO solution, which of the following should be true?

• |__| = +

• |__| = -

• |__| = 0

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Complete the explanation of the error. The student replaced the absolute value with two equations using the positive and negative values of the number on the other side of the equal sign. However, this number was negative.

• An absolute value cannot be equal to a negative number. The equation has no valid solution.

• He should have only used the negative choice, so only

  13/4

  is a valid solution.

• He should have only used the positive choice, so only 27/4 is a valid solution.

• There is no error, so both

  13/4

  and

  27/4

  are valid solutions.

Multiple Choice

Terry is trying to place a satellite dish on the roof of his house at the recommended height of 36 feet. His house is 40 feet

wide, and the height of the roof can be described by the function

h(x) = −32|x − 20| + 30,

where x is the distance along the width of the house. Complete the absolute-value equation and determine where Terry should place the dish.

The satellite dish needs to be 36 feet above the ground.

• Terry should place the satellite dish at one of the edges of the roof,

  x = 0 feet

  or

  x = 40 feet.

• Terry should place the satellite dish at

  x = 10 feet

  or

  x = 30 feet.

• Terry should place the satellite dish at the peak of the roof,

  x = 20 feet.

• There is no place on the roof that is 36 feet high.

Multiple Select

For what type of real-world quantities would the negative-valued answer for an absolute-value equation not make sense? Select all that apply.

• Length

• Bank account balance

• Temperature in

  °F

• Time

• Distance

Multiple Choice

Challenge

This absolute value equation has nested absolute values.

||2x + 9| − 7| = 16

• The solution is

  x = −16 or x = 7.

• The solution is

  x = −16 or x = -7.

• The solution is

  x = 16 or x = 7.

• No solutions

Poll

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