-6r x (12s)

Question

the "x" is a multiplication sign not a variable

Answer 1

 

it should be -72rs

Answer 2

Since both r and s are unknown, you multiply the numbers and letters together: -6 x 12 = -72. r x s = rs, so -6r x 12s = -72rs. SO, how do you solve this? You can't. The best you can do is figure out what r x s is. If you do, then r and s could be any two factors of your answer. For example: if -72rs = 144. rs = 144/-72 = -2. So rs = -2. What are r & s? You can't say for sure. They could be any two factors of -2: 1 & -2, -1/2 & 4, -1 & 2, 1/2 & -4, -1/3 & 6, and so on.

If you tried to continue with rs = -2, this is what would happen:

r = -2/s. Substitute:

-72(-2/s)s = 144.  Work left to right: -72 x -2/s = 144/s.

144/s x s = 144.

144s/s = 144. The s's cancel each other out and you're left with 144 = 144. A true statement, but not very helpful. It doesn't tell you would either r or s is. You could pick any number for s and the statement would still be true. Let's say you pick 10 for s and redo starting from 144s/s = 144.

(144 x 10)/10 = 144

1440/10 = 144

144 = 144. The 10's cancel each other out. You could substitute 1000000 for s and you would still get the same answer, so without knowing for sure what one variable is (r or s), the equation would be unsolvable, regardless of what -72rs would equal.

Answer 3

if you don't have a way to calculate the numerical value of a given variable, then simply multiply the numbers together and use both variables. -6x12=72 so -72rs is what you're looking for if there's no other equation from which you can draw conclusions or plug in variables