SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 1:

tex2html_wrap_inline136

Step1: Isolate the absolute value expression by subtracting 3 from both sides of the equation.

displaymath122



Step 2: Set the quantity within the absolute value notation to tex2html_wrap_inline138 .

eqnarray42



Step 3: Solve for the unknown in both equations.



eqnarray47

eqnarray53



The answers are tex2html_wrap_inline140 and tex2html_wrap_inline142 .



Step 4: Check the solution tex2html_wrap_inline144 by substituting tex2html_wrap_inline140 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_inline150 by substituting tex2html_wrap_inline152 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_inline156 (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_inline158 and tex2html_wrap_inline160 .




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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Author:Nancy Marcus

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