Section 2.7
Absolute Value Equations and
Inequalities
About Absolute Value
• The absolute value of a number is its distance
from 0 on the number line.
• We use two vertical lines |
| to represent
absolute value.
• Absolute value is always non-negative.
Absolute Value Equations
ax  b  k
Three cases:
1. k > 0. Then ax +b = k or
ax + b = -k. Two solutions
2. k = 0. Then ax + b = 0. One
solution.
3. k < 0. No Solution.
You must isolate your absolute value
expression first.
Absolute Value Inequalities
ax  b  k
ax + b > k or ax + b < -k
ax  b  k
ax + b > k or ax + b < -k
ax  b  k
ax + b < k and ax + b > -k
ax  b  k
ax + b < k and ax + b > -k
You must isolate your absolute
value expression first.
Examples
x  14
5 x  1  21
2
x 1  5
3
6x  2  0
13 x  1  3
More Examples
x  3  10
6x 1  2  6
x  5  6  1
Absolute Value on Both Sides
• |ax + b| = |cx + d|
Write two equations:
ax + b = cx + d
ax + b = -(cx + d)
3x  1  2 x  4