Solve & GraphAbsolute Value Inequality

Remember …

Simplify the following:

1. |-5| = 2. |5| =

3. |8 + (-8)| = 4. |8| + |-8|=

What does absolute value mean?

5

5

|0|

= 0 8 + 8

= 16

The distance from zero.

Solve & Check: |2m – 4| = 8

|2m – 4|=8

-8 = 2m - 4

-2 = m m = 6

Solve:

Check: |2(-2) – 4| = 8|-4 – 4| = 8

|-8| = 88 = 8

|2(6) – 4| = 8|12 – 4| = 8

|8| = 88 = 8✔ ✔

2m – 4 = 8+4 + 4-4 = 2m . 2 2

+4 +4 2m = 12 .

2 2

OR

Solve & Check: |3n + 2| - 5 = 4n|3n + 2| - 5 = 4nSolve:

Check:

+ 5 +5|3n + 2| = 4n + 5

-(4n + 5) = 3n + 2 -4n - 5 = 3n + 2

n = -3 n = -1|3(-1) + 2| - 5 = 4(-1) |3(-3) + 2| - 5 = 4(-3)

|-3 + 2| - 5 = -4|-1| - 5 = -4

1 - 5 = -4-4 = -4

|-9 + 2| - 5 = -12|-7| - 5 = -12

7 - 5 = -122 = -12

3n + 2 = 4n + 5

✗

✗

✔

OR -3n + 5 -3n + 5 -7n = 7

-4n - 2 -4n - 2 -n = 3

What does absolute value mean?