SOLVING EQUATION CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.4a:

tex2html_wrap_inline149

Answer: 2.80814296697 and -0.474809633633




Isolate the absolute value term.

eqnarray26




Either tex2html_wrap_inline155 or tex2html_wrap_inline157




Solve tex2html_wrap_inline159

eqnarray36




eqnarray41




eqnarray49




Solve tex2html_wrap_inline159

eqnarray60

eqnarray65

The answers are 2.80814296697 and -0.474809633633. These answers may or may not be solutions to the original equation. You must verify each of the answers.



Check the solutions:



Check the answer x=2.80814296697 by substituting 2.80814296697 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 is equal to the right side of the original equation, the answer x=2.80814296697 is a solution to the original equation.





Check x=-0.474809633633 by substituting -0.474809633633 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 is equal to the right side of the original equation, the answer x=-0.474809633633 is a solution to the original equation.





The solutions are x=2.80814296697and-0.474809633633.





You can also check your answer by graphing

displaymath131
The graph was formed by subtracting the right side of the original equation from the left side of the original equation. You will note that the two x-intercepts on the graph are located at x = 2.80814296697 and -0.474809633633. This verifies the two solutions by a graphical method.


If you would like to review the solution to problem 3.4b, 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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