SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.3d:

tex2html_wrap_inline215

Answer: tex2html_wrap_inline217 -2.19316, 0.666667, and -0.833333




Either tex2html_wrap_inline225 or tex2html_wrap_inline227

Step 1: Solve the equation tex2html_wrap_inline229

eqnarray44

eqnarray60




Step 2: Solve the equation tex2html_wrap_inline231

eqnarray79

eqnarray95




The answers are 2.026498, -2.1931648, 0.666667 and -0.833333.




Step 3: Check the solution x = 2.026498 by substituting 2.026498 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 after we substituted the value 2.026498 for, the solution x = 2.026498 is valid




Check the solution x = -2.1931648 by substituting -2.1931648 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 after we substituted the value -2.1931648 for, the solution x = -2.1931648 is valid.




Check the solution x = 0.666667 by substituting 0.666667 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 after we substituted the value 0.666667 for, the solution x = 0.666667 is valid.




Check the solution x = -0.833333 by substituting -0.833333 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 after we substituted the value -0.833333 for, the solution x = -0.833333 is valid.




You can also check your answer by graphing

eqnarray170

(the left side of the original equation minus the right side of the original equation). You will note that the four x-intercepts on the graph are located at x = 2.026498, -2.1931648, 0.666667 and -0.833333. This verifies our answers.





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Author:Nancy Marcus

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