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​

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

Multiple Choice

Solve the following equation:

|−4 + 5x| = 16

• {16/5,12/5}

• {4, −5}

• {−12/5, 4}

• {4}

Multiple Choice

Solve the following equation:

∣ 2x + 9 ∣ = 15

• x = 3

• x = 3, x = −6

• x = 3, x = −12

• x = 6, x = −12

Multiple Choice

Solve the following equation:

|2a + 10| = 6

• a = 8, a = 2

• a = −2

• a = −8

• a = −8, a = −2

Multiple Choice

Solve the following equation:

|2a − 10| = 6

• a = 8, a = 5

• a = 8

• a = 8, a = −2

• a = 8, a = 2

Multiple Choice

Solve the following equation:

|6 − 2k| = 18

• k = −6, k = 6

• k = −6, k = 12

• k = −6, k = −12

• k = −6, k = 5

Multiple Choice

Solve the following equation:

|v + 8| − 5 = 2

• {−1, −15}

• {−1, −5}

• {−15, 15}

• No Solution

Multiple Choice

Solve the following equation:

−2|−2r − 4| = −12

• {3, 1}

• {−5, 1}

• {−5, 5}

• No Solution

Multiple Choice

Solve the following equation:

3| −8x| + 8 = 80

• {−7/3, 7/3}

• {−3, 3}

• {11/3, −11/3}

• No Solution

Multiple Choice

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.