Multiplication and Division Examples

What's the value of x in the equation 5x – 3x + 9 –  1 = 4(5) – x?

First we simplify each side of the equation:

2x + 8 = 20 – x

Then we add x to each side and subtract 8 from each side:

3x = 12

And finally, we multiply each side of the equation by  (or divide each side by 3, whatever floats your boat):

Solve the equation 

If one-half of y has a weight of 5, then one y has a weight of 5 × 2 = 10. In other words, to get the solution, we multiply both sides of the equation  by 2, or the multiplicative inverse of . In the meantime, we would like to know who's been going around sawing variables in half. Whoever it is had better have a license to do that sort of thing.

Solve the equation .

In words: If one-third of z is 4, then z must be 3 × 4, or 12. Words are nice, but a bit long. Let's stick with numbers.

In symbols:  is the same thing as . One of them just has an additional set of parentheses. We can rewrite the equation and multiply both sides by the multiplicative inverse of , which is 3:

There are two ways to solve the equation -x = 34. What are they?

Way 1: Add x to both sides.

0 = 34 + x

And then subtract 34 from each side.

-34 = x

Way 2: -x equals (-1)x. Since (-1) is a constant, we can multiply both sides of the equation by the multiplicative inverse of -1, which is -1. Wait—a multiplicative inverse doesn't need to be a fraction? No siree. Check it out: -1(-1) = 1. We dig it.

What are two ways to solve the equation -2x = 16?

While we could add 2x to each side and subtract 16 from each side, that's the long way around. The long way around is only good for when there's some beautiful scenery and we've got an hour to kill. Instead, divide each side by -2:

x = -8

All done.