Question

How do you solve `-5k-19=5-13k`?

Answer 1

You have to get all the variables on one side of the equation and all the numbers on the other.
The correct way to 'move' a term, is to add on its inverse to both sides.
The short cut is to put it on the other side and change the sign.

`-5k - 19 color(red)(+ 19) color(blue)(+ 13k) = 5 - 13k color(blue)( + 13k) color(red)(+ 19 )`

The nett effect of this is:
`-5k cancel(- 19 color(red)(+ 19)) color(blue)(+ 13k) = 5 cancel(- 13k color(blue)( + 13k)) color(red)(+ 19 )`

`-5k + 13k = 5 + 19`

`8k = 24 " "` divide both sides by 3.

`k = 3`

The short method would look like this:
`-5k color(red)(- 19) = 5 color(blue)( - 13k) color(red)`

`-5k color(blue)( +13k) = 5 color(red)(+ 19)`

`8k = 24 " "` divide both sides by 3.

`k = 3`