Question

How do you solve `1/(3x) -1/2 = 5/(6x)`?

Answer 1

`x = -1`

Explanation:

The great thing about an equation which has fractions, is that in one easy step we can get rid of the denominators.

Find the LCM (same as the LCD) of the denominators. In this case it is `6x`, because all the denominators are factors of `6x`

Multiply each term in the equation by the LCM of `color(magenta)(6x)`:

`(color(magenta)(6x xx)1)/(3x) -(color(magenta)(6x) xx1)/2 = (color(magenta)(6x)xx5)/(6x)`

Cancel the denominators:

`(cancel(6x)^2 xx1)/(cancel(3x)) -(cancel6^3x xx1)/cancel2 = (cancel(6x) xx5)/cancel(6x)`

This simplifies to give:`" "2 - 3x = 5`

`-3 = 3x`

`x = -1`