Solving Absolute Value Equations

Before (Warm Up)

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

An absolute value equation is

Solve for X

|X|=7

Solve for X

|X| = -3

What would be the correct setup for solving for X?

|X+3| = 5

( EMSAT) Solve for x

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

solve for z.

|3z|+1=10

Solve

∣ 2x + 9 ∣ = 15

Solve

2| x – 3 |+8= 8

An absolute value equation can have which numbers of solutions?

(select all that apply)

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

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

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

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

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

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

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.

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.

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

Challenge

This absolute value equation has nested absolute values.

||2x + 9| − 7| = 16

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