SOLVING EQUATION CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 1:

tex2html_wrap_inline137


Either tex2html_wrap_inline139 tex2html_wrap_inline139 tex2html_wrap_inline139 or tex2html_wrap_inline139 tex2html_wrap_inline141


Step 1: tex2html_wrap_inline139 Solve tex2html_wrap_inline143


eqnarray30



Step 2: tex2html_wrap_inline139 Solve tex2html_wrap_inline141

eqnarray41

There are 4 answers: the approximate answers are tex2html_wrap_inline147 and -1.73205080757, and the exact answers are x = - 3 and 1.



Check the solution x = 1.73205080757 by substituting 1.73205080757 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 1.73205080757 for x, then x = 1.73205080757 is a solution.



Check the solution x = - 1.73205080757 by substituting - 1.73205080757 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 - 1.73205080757 for x, then x = - 1.73205080757 is not a solution.



Check the solution x = - 3 by substituting - 3 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 - 3 for x, then x=-3 is a solution.



Check the solution 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 not equal to the right side of the original equation after we substitute the value 1 for x, then x=1 is not a solution.



The solutions are 1.73205080757 and - 3.




You can also check your answer by graphing

eqnarray101

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


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.

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Author: Nancy Marcus

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