Solving Absolute Value Equations

Multiple Select

What number(s) are 5 units from 0?

• 5

• -5

• 0

• 10

|x| = 5​

is read as "x is 5 units from 0"​

Absolute Value represents a DISTANCE

|-5| = 5

is read as "-5 is 5 units from 0"​

Absolute Value represents a DISTANCE

Multiple Choice

How do you read this?

|x| = 7

• x is 7 units from 0

• 7 is x units from 0

• 0 is 7 units from x

• x is 0 units from 7

Multiple Select

What could the value of x be?

|x| = 7

Choose all that apply.

• 7

• -7

• 14

• 0

​Why does an absolute value equation have two solutions?

​When |3x|=7, how do we solve it?

What could be a rule for solving this equation?

​

​

​

​don't forget... it is read as "3x is 7 units from 0"

​How would you read

​

|x+2| = 5​

​

______ is ____ units from 0​

​How would you read

​

|x+2| = 5​

​

What numbers are 5 units from 0?

​How would you read

​

|x+2| = 5​

​​

So...

x+2 = 5 or x+2 = -5​

Multiple Select

Solve for x

|3x| = 9

Don't forget to choose two answers!

• 3

• -3

• 9

• 27

• -27

Multiple Select

Solve for x

$$\left|\frac{x}{5}\right|=2$$  

Don't forget to choose two answers!

• 10

• -10

• 2

• 5

• $$\frac{2}{5}$$  

Multiple Select

Solve for x

|x+3| = 1

Don't forget to choose two answers!

• 1

• -1

• 2

• -2

• -4

Multiple Select

Solve for x

|x-3| = 5

Don't forget to choose two answers!

• 8

• -2

• 5

• 3

• 2

​How would you read this?

|x| = -2​

Match

Match the following

• |x| = 5

• |2x| = 4

• |x+2| = 6

• |x-3| = 2

• $$\left|\frac{x}{5}\right|=-6$$  

x = 5, -5

x = 2, -2

x = 4, -8

x = 1, 5

No Solution

• x = 5, -5

• x = 2, -2

• x = 4, -8

• x = 1, 5

• No Solution

Multiple Select

Solve for x:

|2x-3| = 5

Choose two answers!!

• 4

• -1

• 1

• -4

• 2

​How does solving absolute value equations differ from what we've been doing?

What about these?

​

2|2x| = 20​ 3|2x|-5 = 20​

Fill in the Blank

Solve for x. Write your answer with a comma between both numbers.

2|x-4| = 6

Match

Match the following

• |x| = 5

• |2x| = -2

• 2|x| = 2

• 4

• $$2\left|\frac{x}{5}\right|-1\ =\ 7$$  

x = 5, -1

No Solution

x = 1, -1

x = 3, 9

x = -20, 20

• x = 5, -1

• No Solution

• x = 1, -1

• x = 3, 9

• x = -20, 20