Question

Amanda tells you that because a variable is in the denominator, the equation three over x plus one over three equals five over six becomes unsolvable. Amanda explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to Amanda how the equation is still solvable and explain your reasoning.

Answer 1

\[\frac{3}{x}+\frac{1}{3}=\frac{5}{6}\]??

Answer 2

yes

Answer 3

ok it is true that there is a variable in the denominator, but so long as the solution isn't zero (which is isn't) you can still solve it
you can't divide by zero, but if \(x\) is some other number then there is no problem

Answer 4

you can solve in three steps
a) subtract \(\frac{1}{3}\) from both sides
b) take the reciprocal of both sides (flip them)
c) multiply both sides by \(3\)

Answer 5

is that all?

Answer 6

yes, three steps is all

Answer 7

so basically plug in a number for zero? buit what number would it be

Answer 8

i wrote the three steps above
none of those steps said "plug in a number for zero" which has no meaning

Answer 9

oh ok... thank you for helping me :)

Answer 10

yw