Teaching Notes 3.8: Solving Absolute Value Equations
To solve absolute value equations, students must first isolate the absolute value expression. They
then must take into account that the expression within the absolute value symbols can be
positive or negative, a fact that affects the solution of the equation. Errors are often made in
both of these procedures.- Explain to your students that absolute value is the number of units a number is from 0 on the
number line. Present examples such as| 3 |=3and|− 5 |=5. Note that the absolute value of
a number is always positive, except| 0 |,whichequals0. - Provide examples of absolute value expressions such as|x− 4 |,| 3 x+ 2 |,and|− 2 x− 10 |.The
absolute value of these expressions cannot be negative even though the expressions inside
the absolute value symbols may be positive or negative. For example, if|x− 4 |=5,x− 4
could equal 5 orx−4couldequal−5. - Review the information and example on the worksheet with your students. Point out that to
isolate the absolute value expression in an equation, they should follow the same procedures
as for isolating a variable. They may need to add the same number to or subtract the same
number from both sides of the equation, or they may need to multiply or divide both sides
of the equation by the same nonzero number. Make sure that your students understand the
steps for solving equations. Note that there are two solutions to the absolute value equation.
Check each solution with your students.
EXTRA HELP:
Be sure to write two equations and solve each of them.ANSWER KEY:
(1)x=8andx=− 8 (2)y=12 andy=− 6 (3)y=8andy=− 7 (4)x=4andx=− 7
(5)y=−3andy= 7 (6)x=−3andx= 3 (7)x=9andx=− 3 (8)x=2andx= 8
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(Challenge)April forgot to isolate the absolute value expression. Because the equation was equal
to zero, she concluded that there was only one solution. She should have found that| 3 x|=3and
thatx=1andx=−1.
------------------------------------------------------------------------------------------102 THE ALGEBRA TEACHER’S GUIDE