Question

How do you solve `1/4t + 5 = 3/4t - 2`?

Answer 1

I found: `t=14`

Explanation:

You can collect terms with `t` on the left and get:
`1/4t-3/4t=-2-5`
`(1-3)/4t=-7`
`-2/4t=-7`
`-1/2t=-7`
rearranging:
`t=14`

Answer 2

I would solve it by multiplying all terms (on both sides) by `4` and then perform the normal arithmetic operations to get `t=14`.
(other people might like working with the fractions).

Explanation:

Given `1/4t + 5 = 3/4t -2`

If we multiply all terms by `4` to get rid of the fractions:
`color(white)("XXXX")` `t + 20 = 3t -8`

We can add `(8-t)` to both sides
`color(white)("XXXX")` `28 = 2t`

Flipping the equation ('cause I like it better that way) and dividing by 2
`color(white)("XXXX")` `t =14`