Denis … how did you get from *x - 2x/9 = 45* to **x(1 - 2/9) = 45**.

This is called factoring.

On the left-hand side of the equation, there are two terms: x and 2x/9. The second term is being subtracted from the first.

Each of these terms contains a factor of x, so x can be "pulled out" and placed in front of grouping symbols. What remains after factoring out the x from each term appears inside the grouping symbols.

Do you remember the Distributive Property? If not, I suggest you google it, and refresh your memory. It's very important to understand, when working with algebraic expressions:

a(b - c) = a·b - a·c

On the left-hand side, we see two quantities being multiplied. One quantity is a; the other is b-c. The Distributive Property tells us, when performing this multiplication, that each term inside the parentheses gets multiplied by the factor outside. The result is shown on the right-hand side.

Well, simple factoring is the reverse of distribution. In other words, we may read the equation above from right to left, too.

Note on the right-hand side that each term contains a factor of a. Therefore, we can factor out the a, by placing it in front of grouping symbols surrounding what remains. We say that the expression on the left-hand side is "factored"; the equivalent expression on the right-hand side is "expanded".

Google

factoring linear binomials, to see more examples of the process. :cool: