SOLVING EQUATION CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 1:

tex2html_wrap_inline197 = tex2html_wrap_inline199

Either

tex2html_wrap_inline201 or tex2html_wrap_inline203

Solve tex2html_wrap_inline205

eqnarray37

eqnarray50

Solve tex2html_wrap_inline207

eqnarray68

eqnarray81

The answers are 7.694933, -0.194933, 3.5 and 1. 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=7.694933 by substituting 7.694933 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 (not completely because we rounded 7.694933) to the right side of the original equation, the answer x=7.694933 is a solution to the original equation.




Check x=-0.194933 by substituting -0.194933 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 (not completely because we rounded -0.194933) to the right side of the original equation, the answer x=-0.194933 is a solution to the original equation.



Check x=3.5 by substituting 3.5 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=3.5 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 equal to the right side of the original equation, the answer x=1 is a solution to the original equation.



The solutions are x=7.694933, -0.194933, 3.5, and 1.




You can also check your answer by graphing

displaymath179

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 four x-intercepts on the graph are located at x=7.694933, -0.194933, 3.5, and 1. This verifies the four solutions by a graphical method.





If you would like to work another problem, click on example.

If you would like to test yourself by working some problems similar to this example, 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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