SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.3c:

tex2html_wrap_inline137

Answer: tex2html_wrap_inline139 and tex2html_wrap_inline141



Solutions:



Either tex2html_wrap_inline143 or tex2html_wrap_inline145



Step 1: Solve tex2html_wrap_inline143

eqnarray42




Step 2: Solve tex2html_wrap_inline149

eqnarray54




The answers are tex2html_wrap_inline139 (rounded) and tex2html_wrap_inline153 *(rounded)




Step 3: Check the solution tex2html_wrap_inline139 by substituting -1.26087 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 -1.26087 is substituted for, then x=-1.26087 is a valid solution.




Check the solution tex2html_wrap_inline153 by substituting -0.67568 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 -0.67568 is substituted for, then x=-0.67568 is a valid solution.




You can also check your answer by graphing tex2html_wrap_inline179 (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_inline181 and tex2html_wrap_inline183 This verifies the solutions.





If you would like to review the answer and solution to problem 3.3d, click on solution.

If you would like to go back to the problem page, click on problem.

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Author:Nancy Marcus

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