SOLVING EQUATIONS
CONTAINING ABSOLUTE VALUE(S)SOLVING EQUATIONS
CONTAINING ABSOLUTE VALUE(S)
Note:
if and only if 
if and only if a
+ b = 3 or a + b = - 3
if any only if a
+ b = + (x + y)
or a + b = - (x+ y)
Solve for x in the following equation.
Example 1:
Either 
or 
Since the left side of the original equation equals the right side of the
original equation after we substituted the value -2 for x, then
x = -2 is
a solution.
Since the left side of the original equation equals the right side of the
original equation after we substituted the value
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Step 1:
Step 2:
The answers are -2 and 
. These answers may
or may not be the solutions.
Step 3: Check the answers:
Check the answer x = - 2 by substituting -2 in the original equation for x.
If the left side of the equation equals the right side of the equation after
the substitution, you have found the correct answer.
Check the answer 
by substituting
in the original equation for x. If the left side of the equation equals the right
side of the equation after the substitution, you have found the correct
answer.
, then
is a solution.
The solutions are x = - 2 and 
You can also check your answer by graphing 
(the left side of the original equation minus the right side
of the original equation). You will note that the two x-intercepts on the
graph are located at -2 and 
This verifies the solution graphically.
If you would like to review another example, click on Example
If you would like to test yourself by working some
problems similar to this example, click on Problem.
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