# Reexpressing equations

1. Oct 20, 2012

### surferbarney0729

I am solving equations for a problem where we must reexpress the equation. I have been given the reexpressed equations, but simply cannot see the steps to quickly change the expression.

The expressions are below

1. Q = 12-2P.. it is reexpressed as P = 6-Q/2
2. Q = 18-P... it is reexpressed as P = 18-Q
3. Q = 8-p/3...it is reexpressed as P = 24-3Q

Can anyone tell me the steps to get from the initial equations to the new expressions?

Thanks

2. Oct 20, 2012

### Staff: Mentor

We normally say "rewrite". I don't think I've ever seen anyone use "reexpress".

When you solve an equation for one variable, you get a new equation.
These are very simple linear equations. Your book must have some examples of solving a linear equation for one variable in terms of another.

3. Oct 20, 2012

### Staff: Mentor

After thinking about this "reexpressing" equations terminology, is this terminology used by your instructor or in the textbook? I don't see the point of it in light of the fact that there already is some perfectly good terminology -- equivalent equations.

In your first example, Q = 12 - 2P and P = 6 - Q/2 are equivalent equations. Any pair of numbers (P, Q) that satisfies the first equation also satisfies the second equation.

4. Oct 21, 2012

### surferbarney0729

This was from a textbook.

We needed to reexpress a demand curve for individuals to attempt to set a new tax rate for each individual.

I was just more or less trying to find another example of how those equations were rewritten(reexpressed) so I could understand all the steps in the text examples

5. Oct 21, 2012

### Mentallic

Ok well for the first we have

Q = 12 - 2P

and we want to make the variable P the subject (which means have it in the form P = ...)

So the first thing we do is take away 12 from both sides,

Q - 12 = 12 - 2P - 12

and notice that on the right side the 12's cancel, so we can simplify that into

Q - 12 = -2P

Now, we have -2 times P, and we want just P, so we can divide by -2 to give

(Q-12)/(-2) = -2P/(-2)

And the right side is now obviously just P. But what we want to do is simplify the left side of the equation.

Well, to do this we have a basic rule of fractions which is

$$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$

so what we end up with is

Q/(-2) -12/(-2) = P

And since -12/-2 = 12/2 = 6 and Q/-2 = -Q/2 we have

6 - Q/2 = P

We can also switch each side of the equality without a problem, so our final answer is

P = 6 - Q/2