1. Absolute Value Equations

2. What is absolute value?
Absolute value is the distance a point is away from zero on the number line.
It is also sometimes called magnitude.

3. What is absolute value?
There are 2 points for every given distance (except for zero)
one in the positive direction
and one in the negative direction.

4. The symbol for absolute value is two vertical lines | |.
| |
The symbol for absolute value is two vertical lines | |.
Be careful that you don’t confuse them with parentheses, which are curvy ( )

5. The absolute value of + 5: | + 5 | = 5
| 5 |
The absolute value of + 5:
| + 5 | = 5
because the point + 5 is 5 units away from zero on the number line.

6. The absolute value of – 5: | - 5 | = 5
because the point - 5 is 5 units away from zero on the number line.

7. The meaning of absolute value
How many numbers are 5 units away from zero on the number line?
| x | = 5
There are 2 answers: both + 5 and - 5

8. Stuffing can either equal + 5 or – 5
Solve this equation!
| x + 2| = 5
| stuffing| = 5
Stuffing can either equal + 5 or – 5
x + 2 = +5 | x + 2 = – 5
x = + 5 – 2| x = – 5 – 2
x = 3| x = -7

9. FIRST: Isolate the Absolute Value
| x + 2|+ 7 = 15
| x + 2| = 15 – 7
|stuffing|= 8
Stuffing can either equal + 8 or – 8
x + 2 = +8 | x + 2 = – 8
x = + 8 – 2 | x = – 8 – 2
x = | x = – 10

10. Whoa! Absolute value can never be negative! Answer is “No Solution”
Trick question
| x + 2|+ 7 = 5
| x + 2| = 5 – 7
|stuffing|= – 2
Whoa! Absolute value can never be negative!
Answer is “No Solution”

11. Absolute Value Means distance from zero or “magnitude”
Always positive or zero since it is a distance.
Absolute value equations – isolate the absolute value
Solve for both + and – on the right
Expect 2 answers.