SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 3:

tex2html_wrap_inline215





Either tex2html_wrap_inline217 tex2html_wrap_inline217 tex2html_wrap_inline217 or tex2html_wrap_inline217 tex2html_wrap_inline219




Step 1: tex2html_wrap_inline217 Solve tex2html_wrap_inline221

eqnarray45



eqnarray64




Step 2: tex2html_wrap_inline217 Solve tex2html_wrap_inline219

eqnarray82



eqnarray96






There are four real answers at tex2html_wrap_inline225 -0.683959382319, 10.1564005278, and -0.65640052777. 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_inline233 by substituting 12.1839593823 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 12.1839593823 for x, then tex2html_wrap_inline243 is a solution.






Check the solution tex2html_wrap_inline245 by substituting -0.683959382319 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 -0.683959382319 for x, then tex2html_wrap_inline245 is a solution.






Check the solution tex2html_wrap_inline257 by substituting 10.1564005278 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 10.1564005278 for x, then tex2html_wrap_inline257 is not a solution.






Check the solution tex2html_wrap_inline269 by substituting -0.65640052777 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 -0.65640052777 for x, then tex2html_wrap_inline269 is not a solution.






The solutions are tex2html_wrap_inline281






You can also check your answer by graphing

eqnarray168

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 tex2html_wrap_inline283 and -0.6839593823. This verifies that the solutions are tex2html_wrap_inline283 and -0.6839593823.


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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