SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 4: tex2html_wrap_inline217

tex2html_wrap_inline184





Either tex2html_wrap_inline217 tex2html_wrap_inline186 tex2html_wrap_inline217 or tex2html_wrap_inline217 tex2html_wrap_inline188





Step 1: tex2html_wrap_inline217 Solve tex2html_wrap_inline190

eqnarray37


eqnarray51







Step 2: tex2html_wrap_inline217 Solve tex2html_wrap_inline190

eqnarray67


eqnarray81







There are four real answers at tex2html_wrap_inline194 0.242810330952, 2.49034517802, and 0.146018458341. However all these answers may or may not be solutions. You must verify that your answers are the solutions to the original equation.





Step 4:Check the solutions:

Check tex2html_wrap_inline202 by substituting 2.62082603268 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 is equal to the right side of the original equation after we substitute the value 2.62082603268 for x, then tex2html_wrap_inline202 is a solution.






Check the solution tex2html_wrap_inline214 by substituting 0.242810330952 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 is not equal to the right side of the original equation after we substitute the value -0.683959382319 for x, then tex2html_wrap_inline214 is not a solution.






Check the solution tex2html_wrap_inline226 by substituting 2.49034517802 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 is not equal to the right side of the original equation after we substitute the value 2.49034517802 for x, then tex2html_wrap_inline226 is not a solution.






Check the solution tex2html_wrap_inline238 by substituting 0.146018458341 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 is equal to the right side of the original equation after we substitute the value 0.146018458341 for x, then tex2html_wrap_inline238 is a solution.






The solutions are 2.62082603268 and 0.146018458341.






You can also check your answer by graphing

eqnarray145

The graph is formed by subtracting the right side of the original equation from the left side of the original equation. Note that the graph has two x-intercepts located at 2.62082603268 and .0.146018458341 This verifies the two solutions.


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

If you would like to go back to the equation table of contents, click on Contents.




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Author: Nancy Marcus

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