SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.



Example 1:

tex2html_wrap_inline85



Step 1:The absolute value is already isolated.

Either 2x-1=+5 or 2x-1=-5



Step 2:Solve the equation 2x-1=+5

eqnarray30




Solve the equation 2x-1=-5

eqnarray34




The answers are 3 and -2. These answers may not be solutions to the equation.




Check the solution x=3 by substituting 3 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 solution 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.



The solutions are x=3 and -2.





You can also check your answer by graphing tex2html_wrap_inline119 (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 3 and -2. This verifies our solutions graphically.


If you would like to work 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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Author:Nancy Marcus

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