SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.3b:

tex2html_wrap_inline131

Answer: tex2html_wrap_inline133 and x=-1

Solutions:

Either tex2html_wrap_inline137 or tex2html_wrap_inline139

Step 1: Solve tex2html_wrap_inline137

eqnarray40




Step 2: Solve tex2html_wrap_inline143

eqnarray54





The answers are tex2html_wrap_inline145 and x = -1.

Step 3: Check the solution tex2html_wrap_inline145 by substituting 0.333333 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 0.333333 is substituted for, then x = 0.333333 is a valid solution.




Check the solution x=-1 by substituting -1 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 is substituted for, then x=-1 is a valid solution.




You can also check your answer by graphing tex2html_wrap_inline173 (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_inline175 and -1. This verifies the solutions.


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

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

If you would like to go back to the equation table of contents, click on contents.

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Author:Nancy Marcus

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