Question

How do you solve `12r-18=13r+18`?

Answer 1

`r = -36`

Explanation:

Re-arrange the equation by moving all the like terms to one side and the numbers or constants to the other side.

`12r color(red)(-12r) -18 color(blue)(-18) = 13r color(red)(-12r)+18 color(blue)(-18)`

Use additive inverses to remove a term from a side where you do not want it. Do the same operation on each side of the equation.
Simplifying both sides gives:

`-36 = r " "hArr" "r = -36`

Note that by moving the variable to the right side, we ended up with a positive variable.

Otherwise we would have ended up with

`-r = 36" "larr` this is not wrong, but requires an extra step

`r = -36" "larr div -1`