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```2.4 & 2.5
Absolute Value Inequalities and
Equations
Learning Goals
• Interpret complicated expressions by viewing one or
more of their parts as a single entity
• Create equations and inequalities in one variable and
use them to solve problems
absolute value: distance from zero on a number line
Ex 1
15  3x  6
Ex 2
2 x9 37
extraneous solution: a solution to a transformed
equation but not the original equation
Ex 3
5x  2  7x  14
Ex 4
3x  4  4x 1
Ex 5
x  x 1
Absolute Value Inequalities
a b
b  a  b
x  5 distance within 5 units in both directions
a b
a  b or a  b
x  5 distance outside 5 units in both directions
Ex 6
3x  4  8
Ex 7
5x  10  15
Ex 8
 2 x  1  5  3
Ex 9
x  5  2
Ex 10
x  5  2
Write each compound inequality as
an absolute value inequality.
Ex 11
12  m  20
Ex 12
x  1 or x  4
Absolute Value Statements
symbols
definition
distance from x to 0 is a
units
distance from x to 0 is
less than a units
distance from x to 0 is
greater than a units
graph
With a partner, graph each solution
x  5 and x  6
x  6 or x  5
x5  x
```
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