Absolute Value Equations & Inequalities
Absolute Value - ________________________ a number is from __________
Interpreting Absolute Value Equations:
|x| = |x – 0| = k means that the distance
between x and 0 is ___.
|x – b| = k means that the distance
between x and b is ___.
Graph:
Graph:
0
b
Solutions: __________ or ___________
Solutions: __________ or ___________
Ex 1 Solve and graph |x| = 7.
Ex 2 Solve and graph |x - 17| = 38.
Ex 3 Solve and check |6x + 5| = 13
Ex 4 Solve and check |x + 7| = -11
Notice: If c < 0, there is ____________________ to the absolute value equation!
Extraneous Solution - an apparent solution that is _________________ because it
doesn’t satisfy the original equation
Ex 5 Solve and check |3x – 24| = 5x
Absolute Value Inequalities: c > 0
Inequality
Meaning in words:
 ax + b is __________ c and -c.
|ax + b| < c  ________ statement
 ax + b is __________ c and -c.
|ax + b| > c  ________ statement
Equivalent Statement:
Graph:
Ex 6 Rewrite the following absolute value inequalities as compound inequalities.
a) |x – 8| < 3
b) |x + 5| < 7
c) |x + 2| > 9
d) |x – 6| > 1
To solve absolute value inequalities:
1. Isolate ____________
2. Rewrite using an equivalent __________________________________.
3. Solve using inverse operations.
Ex 7 Solve and graph the following absolute value inequalities.
a) |3x - 2| > 18
b) 2|-x + 5|-1 < 6
Ex 8 Write an absolute value inequality that describes the following situations.
a) A manufacturer has a 0.6 oz tolerance
b) A manufacturer has a tolerance of 0.36
for a bottle of salad dressing advertised
pounds (lb) for a bag of potting soil that
as 16 oz. Write and solve an absolute value advertised as 9.6 lb. Write and solve an
inequality that describes acceptable
absolute value inequality that describes
volumes for "16 oz" bottles.
unacceptable weights for "9.6 lb" bags.
Ab. Val. Inequality:_________________
Ab. Val. Inequality:__________________
Question: How are absolute value equations and inequalities like linear equations and
inequalities?