SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.5c:

tex2html_wrap_inline212



Answer: tex2html_wrap_inline214 tex2html_wrap_inline214



Solution:

Either tex2html_wrap_inline214 tex2html_wrap_inline216 tex2html_wrap_inline214 ortex2html_wrap_inline214 tex2html_wrap_inline218





Step 1: tex2html_wrap_inline214 Solve tex2html_wrap_inline220

eqnarray37


eqnarray47

Step 2: tex2html_wrap_inline214 Solve tex2html_wrap_inline218

eqnarray62


eqnarray72





There are four real answers; tex2html_wrap_inline224 However all these answers may or may not be solutions. You must verify that your answers are the solutions to the original equation.





Step 4:Check the solutions:

Check tex2html_wrap_inline214 by substituting 2.24455 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 after we substitute the value 2.24455 for x, then tex2html_wrap_inline214 is a solution.





Check the solution tex2html_wrap_inline238 by substituting -0.04455 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 after we substitute the value -0.04455 for x, then tex2html_wrap_inline238 is not a solution.





Check the solution tex2html_wrap_inline250 by substituting 2.153565 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 after we substitute the value 2.153565 for x, then tex2html_wrap_inline250 is not a solution.





Check the solution tex2html_wrap_inline262 by substituting x=0.046435 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 after we substitute the value tex2html_wrap_inline262 for x, then tex2html_wrap_inline262 is not a solution.







There is one solution: tex2html_wrap_inline214

You can also verify these two real answers by graphing

eqnarray155

The graph is formed by subtracting the right side of the original equation from the left side of the original equation. Note that there is one x-intercept at 2.24455. This verifies the solutions.




If you would like to review the solution to problem 3.5d, click on Solution

If you would like to go back to the problem page, click on Problem

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Author:Nancy Marcus

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