SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 2:

tex2html_wrap_inline127

Either tex2html_wrap_inline129 or tex2html_wrap_inline131




Step 1: Solve tex2html_wrap_inline129

eqnarray26




Step 2: Solve 5 x + 7 = - (2x + 11) :

eqnarray32




The answers are tex2html_wrap_inline137 and tex2html_wrap_inline139 .



Step 4: Check the solution tex2html_wrap_inline141 by substituting tex2html_wrap_inline137 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 when tex2html_wrap_inline137 is substituted for, then tex2html_wrap_inline141 is a valid solution.




Check the solution tex2html_wrap_inline153 by substituting tex2html_wrap_inline139 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 when tex2html_wrap_inline139 is substituted for, then tex2html_wrap_inline153 is a valid solution.




You can also check your answer by graphing tex2html_wrap_inline165 (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_inline167 and tex2html_wrap_inline169


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Author:Nancy Marcus

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