FLC
4.3
Math 120 Intermediate Algebra
Absolute Value Equations and Inequalities
Defn The absolute value of , denoted
, is defined as
.
The Absolute Value Principle for Equations
Let
be a positive number and let be an algebraic expression.
a) The solutions of
are those that satisfy
or
b) The equation
is equivalent to
.
c) The equation
has no solution.
.
Principles for Solving Absolute Value Problems
Let
be a positive number and let be an algebraic expression.
a) The solutions of
are those that satisfy
or
b) The solutions of
are those numbers that satisfy
c) The solutions of
are those numbers that satisfy
.
d) The solutions of
are those numbers that satisfy
.
Ex 1 Solve.
a)
Ex 2 Let
Ex 3 Solve.
a)
.
.
or
and
b)
. Find all
for which
.
b)
Ex 4 Solve and graph.
a)
b)
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