SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.3a:

tex2html_wrap_inline110

Answer: tex2html_wrap_inline112 and tex2html_wrap_inline114

Solutions:

Either tex2html_wrap_inline116 or tex2html_wrap_inline118

Step 1: Solve tex2html_wrap_inline116

eqnarray34

Step 2: Solve tex2html_wrap_inline122

eqnarray40



The answers are tex2html_wrap_inline112 and. tex2html_wrap_inline126




Step 3: Check the solution tex2html_wrap_inline128 by substituting -7.666667 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 -7.666667 is substituted for, then x = -7.666667 is a valid solution.




Check the solution x = 1.8 by substituting 1.8 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 1.8 is substituted for, then x=1.8 is a valid solution.




You can also check your answer by graphing tex2html_wrap_inline152 (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_inline154 and tex2html_wrap_inline156


If you would like to review the answer and solution to problem 3.3b, 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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