Question

How do you solve `11/3x-1/4=2`?

Answer 1

`x = 27/44`

Explanation:

Your first goal here is to make sure that all the fractions have the same denominator. As given, the equation looks like this

`11/3x - 1/4 = 2/1`

Now, the common denominator for `3`, `4`, and `1` is `12`, so you will need to multiply the first fraction by `1 = 4/4`, the second fraction by `1 = 3/3`, and the third fraction by `1 = 12/12`.

This will get you

`11/3x * 4/4 - 1/4 * 3/3 = 2/1 * 12/12`

You now have three fractions with equal denominators

`(11 * 4)/12x - (1 * 3)/12 = (2 * 12)/12`

`44/12x - 3/12 = 24/12`

You can now focus exclusively on the numerators and say that

`44 * x - 3= 24`

Add `3` to both sides of the equation

`44 * x - color(red)(cancel(color(black)(3))) + color(red)(cancel(color(black)(3))) = 24 + 3`

`44 * x = 27`

Divide both sides of the equation by `44` to get

`(color(red)(cancel(color(black)(44))) * x)/color(red)(cancel(color(black)(44))) = 27/44`

`x = 27/44`

Do a quick double-check to make sure that the calculations are correct

`11/3 * 27/44 - 1/4 = 2`

`(11 * 9)/44 - 1/4 = 2`

`9/4 - 1/4 = 2`

`8/4 = 2" "color(darkgreen)(sqrt())`