SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:

Solve for x in the following equation.



Solve for x in the following equation.


Problem 1c:

tex2html_wrap_inline101



Answer: tex2html_wrap_inline217 No solution.



Note that the absolute value of an expression can never equal a negative number. There is no solution.


Suppose you did not make this observation and went ahead with the solution. You will catch it in the check because the solutions will not check.





Step 1: tex2html_wrap_inline217 Set the quantity within the absolute value notation to tex2html_wrap_inline217 tex2html_wrap_inline103

eqnarray32



Step 2: tex2html_wrap_inline217 Solve for x in the equation 10x - 3 = - 7 :

eqnarray35


tex2html_wrap_inline217 tex2html_wrap_inline217 Solve for x in the equation 10x - 3 = 7:

eqnarray40

The indicated answers are 1 and tex2html_wrap_inline111 . These answers may not be solutions to the original equation; you must verify the solutions.





Step 3:tex2html_wrap_inline217Check the solutions.

Check the answer 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 does ot equal the right side of the original equation after we substituted the value 1 for x, x=1 is not a solution.





Check the solution tex2html_wrap_inline125 by substituting tex2html_wrap_inline111 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 does ot equal the right side of the original equation after we substituted the value tex2html_wrap_inline111 for x, tex2html_wrap_inline125 is not a solution.





There are no solutions.




You can also check your answer by graphing tex2html_wrap_inline137 (the left side of the original equation minus the right side of the original equation). You will note that the there are no intercepts on the graph. There are no solutions.



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Author:Nancy Marcus

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