SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 3:

tex2html_wrap_inline191


Step 1:tex2html_wrap_inline217 The absolute value is already isolated.

Step 2:tex2html_wrap_inline217 Set the quantity within the absolute value notation to tex2html_wrap_inline217 tex2html_wrap_inline193

eqnarray36


or


eqnarray36





Step 3:tex2html_wrap_inline217 Solve for x in the equation tex2html_wrap_inline217 tex2html_wrap_inline195 :


eqnarray57





Step 4:tex2html_wrap_inline217 Solve for x in the equation tex2html_wrap_inline217 tex2html_wrap_inline197 :

eqnarray86

The answers are tex2html_wrap_inline199 and tex2html_wrap_inline201 .





Step 5:tex2html_wrap_inline217Check the solutions.


Check the solution x = tex2html_wrap_inline199 by substituting tex2html_wrap_inline199 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.





Step 6:tex2html_wrap_inline217 Check the solution x = tex2html_wrap_inline201 by substituting tex2html_wrap_inline201 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.





You can also check your answer by graphing tex2html_wrap_inline219 (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 tex2html_wrap_inline221 and tex2html_wrap_inline223




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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