Luttrell 2012
78
Name: ______________________
Date: _____
5e – Graphing Absolute Values
Sometimes it is quite impossible to simplify absolute equations unless you get rid of them
altogether. That is done only by finding two equivalent equations and solving each. The reason
for two equations is because the expression inside the absolute value could very well be a
positive or negative value. Now if the expression were positive, the absolute values are
redundant and can simply be dropped. But if the expression were negative, the only way to
make it positive like an absolute value would be to negate the expression.
E
x
ample: |-
x
+ 2 | ≤ 5
|
x
- 3 | > 2
+(-
x
+ 2)
≤5 and -(-
x
+ 2) ≤5
x
- 3 >2 or -(
x
- 3) >2
-
x
≤3 and
x
-
2 ≤ 5
x
> 5 or
x
- 3 < -2
x
≥-3 and
x
≤ 7
x
>5 or
x
< 1
| ● | | | | | | | | | ● |
| | |
◯
| | |
◯
|
- 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -1 0 1 2 3 4 5 6
E
x
plain why
and
is used in the first e
x
ample and
or
in the second. ________________________
_____________________________________________________________________________
Simplify each expression and graph the solution.
1. x = |-2|
2. x = | -5|
3. |x| = 4
4. |x| = 2
5. x < |- 3|
6. x ≥ |-1|
7. |x| ≤3
8. |x| ≥7
Solve each equation by converting into two equivalent equations first. Graph the solution.
9. | x – 3 | = 5
10. | x – 1 | = 4
11. | x – 5 | = 6
12. |x – 2 | = 3
