- Thread starter marsrg7
- Start date

- Joined
- Oct 6, 2005

- Messages
- 10,158

What do you do when solving equations for x, if x is multiplied by some factor?

EG:

4x = a

In other words, what operation would you carry out to both sides of the equation, in order to isolate x ?

Use the same reasoning to isolate c, in your exercise.

- Joined
- Oct 6, 2005

- Messages
- 10,158

This is why we need to understand the meaning of "factors".marsrg7 said:4x=a subtract 4 from both sides? No.

We call 4x a "product" because two things are being multiplied together.

4x literally means "the number 4 times the number x".

(We could also write it as 4*x, to show the multiplication sign, but 4x is understood to mean the same thing.)

Now, both the number 4 and the number x are called the "factors" of the product 4x.

When we are trying to isolate x from another factor, we must

4x = a

Divide both sides by 4.

(4x)/4 = a/4

On the lefthand side, the fours cancel, right? (They cancel because 4/4 is the same as 1.)

x = a/4

Now I will show you an example where we WOULD subtract 4 from both sides.

x + 4 = a

To solve this for x, we want to isolate x. Since the 4 is being ADDED (not multiplied), we would get rid of it on the lefthand side by subtracting. Of course, whatever we do to one side of an equation, we must do to the other side.

Subtract 4 from both sides.

x + 4 - 4 = a - 4

Simplify.

x = a - 4

Going back to your exercise, we have:

xy = abc

Each of the unknown numbers a, b, c, x, and y are factors because they are being multiplied (not added or subtracted).

I can show these multiplications using a multiplication sign.

x*y = a*b*c

You're asked to solve for c, so you want to isolate c by itself on one side.

We cannot subtract the a and b, for the reason discussed above. They are factors.

We need to use division.

We can get rid of the a and b on the righthand side by dividing by a*b (or ab).

xy = abc

Divide both sides by ab.

(xy)/(ab) = (abc)/(ab)

Do you "see" how the common factors of ab on top and bottom cancel?

c = (xy)/(ab)

(BTW: I used parentheses to clearly show what's in the numerators and what's in the denominators.)

- Joined
- Oct 6, 2005

- Messages
- 10,158

This is a proportion (two ratios set equal to one another).

Start by cross-multiplying.

Then, use division (just like the previous exercise), to isolate B.

Please show your work, if you want more help.