SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)



Note:


Solve for x in the following equation.



Problem 3.2a :

tex2html_wrap_inline134

Step1: Isolate the absolute value expression by adding 8 to both sides of the equation.





Step 2: Set the quantity within the absolute value notation to tex2html_wrap_inline136 .



Step 3: Solve for x in both equations.




The answers are tex2html_wrap_inline138 and -1.



Step 4: Check the solution tex2html_wrap_inline140 by substituting tex2html_wrap_inline138 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:





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 :





You can also check your answer by graphing tex2html_wrap_inline150 (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_inline152 and -1.




If you would like to review the solution and answer to problem 3.2b, click on Solution.

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