SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.


Problem 3.1b:

tex2html_wrap_inline146

Step 1:The absolute value is already isolated.



Step 2:Set the quantity within the absolute value notation to tex2html_wrap_inline148


eqnarray34



Step 3:Solve for x in the equation 3 tex2html_wrap_inline150 :



eqnarray43



Solve for x in the equation tex2html_wrap_inline152 :

eqnarray52



The answers are tex2html_wrap_inline154 and tex2html_wrap_inline156 .



Step 4:Check the solutions.


x = tex2html_wrap_inline154 by substituting tex2html_wrap_inline154 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 after we substituted tex2html_wrap_inline154 for x, this confirms that tex2html_wrap_inline168 is a valid solution.





Check the solution x = tex2html_wrap_inline156 by substituting tex2html_wrap_inline156 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 after we substituted tex2html_wrap_inline156 for x, this confirms that tex2html_wrap_inline180 is a valid solution.






You can also check your answer by graphing tex2html_wrap_inline182 (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_inline184 and tex2html_wrap_inline186


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