SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)


Note:

Solve for x in the following equation.

Example 4 :

tex2html_wrap_inline103



Step1: Isolate the absolute value expression by subtracting 5 from both sides of the equation.

eqnarray14




Step 2: Set the quantity within the absolute value notation to tex2html_wrap_inline105 .

eqnarray30




Step 3: Solve for x in both equations:

eqnarray40



The answers are 7 and tex2html_wrap_inline107 . These answers may not be solutions to the equation. You must verify the answers.



Step 4: Check the solutions.



Check the answer x=7 by substituting 7 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:

Since the left side of the original equation equals the right side of the original equation after the value 7 is substituted for x, we have verified the solution x=7.




Check the answer x=-9.8 by substituting -9.8 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.

Since the left side of the original equation equals the right side of the original equation after the value -9.8 is substituted for x, we have verified the solution =-9.8.




You can also check you answer by graphing tex2html_wrap_inline125 (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 7 and -9.8.

If you would like to test yourself by working some problems similar to this example, click on Problems .

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