Question

help pleaseeee :) Solve for x: 3 over x minus 2 over 3 equals 5 over 6

Answer 1

\[\frac{3}{x} - \frac{2}{3} = \frac{5}{6}\]With problems like this, you can either find a common denominator, or just "clear" the fractions entirely. I prefer the latter. To do so, multiply by the product of all of the denominators:
\[\frac{3}{x}*3*6*x - \frac{2}{3}*3*6*x = \frac{5}{6}*3*6*x\]That gives you (after canceling common factors between numerator and denominator)\[3*3*6-2*6*x=5*3*x\]or\[54-12x=15x\]I bet you can solve that, right?

Answer 2

You could be clever in this case and notice that 6 is a multiple of 3, so you could have only multiplied by 6*x and gotten an equivalent result. Then your equation would have turned out to be \(18-4x=5x\). \(x\) is the same value.

Answer 3

mmm...no.
\[54-12x=15x\]what happens if you add 12x to each side?

Answer 4

\[54-12x+12x = 15x + 12x\]\[54=27x\]
\[x=\]

Answer 5

there you go. you should figure out where you went wrong when you got 6...

Answer 6

always try to learn from your mistakes!