SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.5a: tex2html_wrap_inline217

tex2html_wrap_inline313





Answer: tex2html_wrap_inline217 tex2html_wrap_inline315





Either tex2html_wrap_inline217 tex2html_wrap_inline319 tex2html_wrap_inline217 or tex2html_wrap_inline217 tex2html_wrap_inline321





Step 1: tex2html_wrap_inline217 Solve tex2html_wrap_inline323

eqnarray33


eqnarray38





Step 2: tex2html_wrap_inline217 Solve tex2html_wrap_inline323

eqnarray52


eqnarray57







There are four answers: tex2html_wrap_inline327 0.115562689514, tex2html_wrap_inline331 and tex2html_wrap_inline333 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: tex2html_wrap_inline217 Check the solutions:

Check tex2html_wrap_inline335 by substituting 2.88443731049 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 2.88443731049 for x, then tex2html_wrap_inline335 is a solution.







Check the solution tex2html_wrap_inline347 by substituting 0.115562689514 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 0.115562689514 for x, then tex2html_wrap_inline347 is a solution.







Check the solution tex2html_wrap_inline361 by substituting tex2html_wrap_inline331 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_inline369 for x, then tex2html_wrap_inline371 is not a solution.







Check the solution tex2html_wrap_inline373 by substituting tex2html_wrap_inline375 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_inline375 for x, then tex2html_wrap_inline383 is not a solution.







The solutions are tex2html_wrap_inline315 and 0.1155626895142.




You can also check your real answers by graphing

eqnarray242

The graph is formed by subtracting the right side of the original equation from the left side of the original equation.
Note that the graph has two x-intercepts located at tex2html_wrap_inline315 and 0.1155626895142 This verifies the two real solutions.


If you would like to review the solution to problem 3.5b, 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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