SOLUTION: A student claims that the equation 5x = 4x is a contradiction, since dividing both sides by x leads to 5 = 4, a false statement. Explain why the student is incorrect.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: A student claims that the equation 5x = 4x is a contradiction, since dividing both sides by x leads to 5 = 4, a false statement. Explain why the student is incorrect.      Log On


   

Question 94892: A student claims that the equation 5x = 4x is a contradiction, since dividing both sides by x leads to 5 = 4, a false statement. Explain why the student is incorrect.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Because if x equals zero the equation becomes:
.
5*0 = 4*0
.
and this reduces to:
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0 = 0
.
and this is true. (And if x is allowed to equal zero, you cannot divide both sides by
x because division by zero is not allowed.)
.
So there you have an exception to what the student proposed, so the student is incorrect.
.
Hope this makes sense to you.