Dec. 6 - Absolute Value Equations

Absolute ValueThe distance away from 0

0 5-5 10-10

6 6𝑥=−6 𝑥=6

Absolute ValueThe distance away from 0

0 5-5 10-10

10 10𝑥=−10 𝑥=10

Absolute ValueWhat two points are 5 away from

0?

0 5-5 10-10

Solving Absolute Value

|𝑦−1|=3 is 3 units from 0

0 5-5 10-10

𝑦−1=3𝑦−1=−3

Solving Absolute Value

|3 𝑥|=6To solve (when the absolute value is by itself), split into two equations:• One with a positive 6• The other with a

negative 6

Then solve each individually

3 𝑥=6 3 𝑥=−6

Solving Absolute Value

|𝑛|+3=5To solve (when the absolute value is by itself), split into two equations:• One with a positive• The other with a

negative

Then solve each individually

Negative distance?

Thinking about absolute value as the distance from 0, where would we graph p?

TRICK QUESTION! YOU CAN’T HAVE A NEGATIVE DISTANCE!

This creates a no solution

0 5-5 10-10

Check for Understanding

What’s the solution to

NO SOLUTION, an absolute value makes everything positive, so it cannot

equal a negative number

Check for Understanding

What’s the solution to

NO SOLUTIONRemember, an absolute value has to equal a positive number

Guided Practice

|𝑚|+4=19𝑚=15 𝑚=−15

𝑚=15𝑜𝑟𝑚=−15

1. Isolate the Absolute Value

2. Split into two equations

3. Solve each equation

4. CHECK THE ANSWERS!

1. Isolate the Absolute Value

2. Split into two equations

3. Solve each equation

4. CHECK THE ANSWERS!

Guided Practice

1=|𝑔+1|1=𝑔+1 −1=𝑔+1𝑔=0𝑜𝑟𝑔=−2

Guided Practice

2|𝑑+3|=8𝑑1. Isolate the Absolute Value

2. Split into two equations

3. Solve each equation

4. CHECK THE ANSWERS!• When you check , you get that the absolute value is

equal to a negative number, therefore, is not a solution

𝑑+3=4𝑑

Summary

What are the steps to solve an absolute value equation?1. Is the Absolute Value alone?2. Split the Absolute Value into two

equations3. Solve each equation individually4. Check your answers by plugging

them in!

SummaryOn a half sheet of paper, solve the following to turn in as your ticket out the door. John Doe

D812/6/11

Exit Ticket