Quandaries and Queries


When I have a problem like (2x + 3)/5 = (x + 1)/6 and the question asks to check for extraneous solutions, how do you solve that?




Hi Nicole,

Asking you to check for extraneous solutions is just asking you to do something you should routinely do anyway, that is check your answers. If you solve this equation you get

12 x + 18 = 5 x + 5
7x = -13
x = -13/7

Now check by substituting x = -13/7 into each side of the original equation. In both cases I got -1/7 and hence x = -13/7 is a valid solution.

Where you might see an extraneous solution is situations where you have to square both sides to reach a solution or where you have a fraction with an algebraic expression in the denominator. There is an example of each case in the answer to a previous question.



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