SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.1a:

tex2html_wrap_inline107



Step 2:Set the quantity within the absolute value notation to tex2html_wrap_inline109


eqnarray31



Step 3:Solve for x in the equation 4x-7=3:



eqnarray34



Step 4:Solve for x in the equation 4x-7=-3:



eqnarray39



The answers are tex2html_wrap_inline115 and x=1. However these answers may not be the solutions to the original equation. You must check your answers.


Step 5:Check the solutions.


Check the solution tex2html_wrap_inline115 by substituting tex2html_wrap_inline121 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 tex2html_wrap_inline121 for, the solution tex2html_wrap_inline115 is valid




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 after we substituted the value 1 for, the solution x=1 is valid






You can also check your answer by graphing tex2html_wrap_inline141 (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_inline143 and 1



If you would like to review the solution to problem 3.1b, 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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