SOLVING EQUATION CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.4c:

tex2html_wrap_inline169




Answer: 2 and 1.31774468788




Either tex2html_wrap_inline175 or tex2html_wrap_inline177




Solve tex2html_wrap_inline179

eqnarray31





eqnarray35





eqnarray39





eqnarray47





Solve tex2html_wrap_inline177

eqnarray62





eqnarray67





eqnarray73





The answers are 2,-1, 1.31774468788 and -1.51774468788. 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 by substituting 2 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 is a solution to the original equation.





Check 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 is not equal to the right side of the original equation, the answer x=-1 is not a solution to the original equation. You could also note that the absolute value cannot be negative, therefore no negative answer is valid.





Check x=1.31774468788 by substituting 1.31774468788 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=1.31774468788 is a solution to the original equation.





Check x=-1.51774468788 by substituting -1.51774468788 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 not equal to the right side of the original equation, the answer x=-1.51774468788 is not a solution to the original equation. You could also make the observation that the absolute value of a number cannot be negative, therefore no negative answer is valid.





The solutions are 2 and 1.31774468788.



You can also check your answer by graphing the function

eqnarray122

on your graphing calculator. 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 and 1.31774468788. This verifies the two solutions by a graphical method.


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