SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 2:

tex2html_wrap_inline333




Either tex2html_wrap_inline335 tex2html_wrap_inline335 tex2html_wrap_inline335 or tex2html_wrap_inline335 tex2html_wrap_inline337




Step 1: tex2html_wrap_inline335 Solve tex2html_wrap_inline339

eqnarray30



eqnarray37





Step 2: tex2html_wrap_inline335 Solve tex2html_wrap_inline337

eqnarray51


eqnarray57







There are two real answers at tex2html_wrap_inline343 and 0.219223593596,

and two imaginary answers at tex2html_wrap_inline347 and tex2html_wrap_inline349





Check the solution tex2html_wrap_inline343 by substituting 2.2807764064 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 2.2807764064 for x, then tex2html_wrap_inline343 is a solution.





Check the solution tex2html_wrap_inline363 by substituting 0.219223593596 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 0.219223593596 for x, then tex2html_wrap_inline363 is a solution.





Check the solution tex2html_wrap_inline347 by substituting tex2html_wrap_inline377 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_inline377 for x, then tex2html_wrap_inline347 is not a solution.





Check the solution tex2html_wrap_inline391 by substituting tex2html_wrap_inline393 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.

eqnarray221

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_inline393 for x, then tex2html_wrap_inline391 is not a solution.





The solutions are 1.73205080757 and -3.





You can also check the real answers by graphing

eqnarray258

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 1.73205080757 and 1-3. This means that the two real solutions are 1.73205080757 and -3.


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

If you would like to test yourself by working some problems similar to this example, click on Problem.

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Author: Nancy Marcus

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