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

Sep 25, 2016

$r = - 36$

Explanation:

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

$12 r \textcolor{red}{- 12 r} - 18 \textcolor{b l u e}{- 18} = 13 r \textcolor{red}{- 12 r} + 18 \textcolor{b l u e}{- 18}$

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:

$- 36 = r \text{ "hArr" } r = - 36$

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

Otherwise we would have ended up with

$- r = 36 \text{ } \leftarrow$ this is not wrong, but requires an extra step

$r = - 36 \text{ } \leftarrow \div - 1$