SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 1:

tex2html_wrap_inline112

Either tex2html_wrap_inline114 or tex2html_wrap_inline116




Step 1: Solve tex2html_wrap_inline118

eqnarray25




Step 2: Solve 2 x - 1 = -(4x + 3).

eqnarray29




The answers are -2 and tex2html_wrap_inline124 . These answers may or may not be the solutions.



Step 3: Check the answers:




Check the answer x = - 2 by substituting -2 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 equals the right side of the original equation after we substituted the value -2 for x, then x = -2 is a solution.




Check the answer tex2html_wrap_inline138 by substituting tex2html_wrap_inline124 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 equals the right side of the original equation after we substituted the value tex2html_wrap_inline124 , then tex2html_wrap_inline138 is a solution.




The solutions are x = - 2 and tex2html_wrap_inline152




You can also check your answer by graphing tex2html_wrap_inline154 (the left side of the original equation minus the right side of the original equation). You will note that the two x-intercepts on the graph are located at -2 and tex2html_wrap_inline158 This verifies the solution graphically.


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Author:Nancy Marcus

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