SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.



Example 2:

tex2html_wrap_inline137


Step1: Isolate the absolute value expression by adding 8 to both sides of the equation.



Step 2: Set the quantity within the absolute value notation to tex2html_wrap_inline139 .

eqnarray43


Step 3: Solve for x in both equations.

eqnarray54

The answers are tex2html_wrap_inline141 and tex2html_wrap_inline143 .


Step 4: Check the solution tex2html_wrap_inline145 by substituting tex2html_wrap_inline141 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:





Check the solution tex2html_wrap_inline151 by substituting tex2html_wrap_inline153 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_inline157 (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_inline159 and tex2html_wrap_inline161 .


If you would like to go 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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