SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 4:

tex2html_wrap_inline162

Either tex2html_wrap_inline164 or tex2html_wrap_inline166




Step 1: Solve the equation tex2html_wrap_inline168

eqnarray42

eqnarray58




Step 2: Solve the equation tex2html_wrap_inline170

eqnarray73




The answers are 2.44832565604 and -1.53165898938.




Step 4: Check the solution x = 2.44832565604 by substituting 2.44832565604 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 2.44832565604 for, the solution x=2.44832565604 is valid




Check the solution x = - 1.53165898938 by substituting -1.53165898938 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 -1.53165898938 for, the solution x = -1.53165898938 is valid




You can also check your answer by graphing tex2html_wrap_inline200 (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 = 2.44832565604 and x = -1.53165898938. This verifies our answers.



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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