SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 3:

tex2html_wrap_inline112

Either tex2html_wrap_inline114 or tex2html_wrap_inline116




Step 1: Solve the equation tex2html_wrap_inline118

eqnarray26




Step 2: Solve the equation tex2html_wrap_inline120

eqnarray32




The answers are tex2html_wrap_inline122 and tex2html_wrap_inline124 .




Step 3: Check the solution x = -0.3 by substituting -0.3 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.

Since the left side of the original equation after we substituted the value - 0.3 for, the solution x = -0.3 is valid.




Check the solution x = tex2html_wrap_inline124 by substituting tex2html_wrap_inline124 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 after we substituted the value tex2html_wrap_inline124 for, the solution tex2html_wrap_inline148 is valid.




You can also check your answer by graphing tex2html_wrap_inline150 (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 x = -0.3 and tex2html_wrap_inline154


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Author:Nancy Marcus

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