Solving Equations and Formulas Chapter 2 section 6

Solving for a specific Variable Sometimes equations involve multiple variables, or letters that stand for specific things, such as scientific formulas and physics equations

Geometry Formulas: The formula for Circumference of a circle is: C=2πr (2 x pi x radius) We can solve the formula for r: (this means get r by itself!)

What do you think we could do? If the equation is set up as If the equation is set up as C = 2πr, and you are asked to get r by itself, then you need to first ask yourself: What is attached to r? How can you “undo” the operation? Since 2π is “stuck” to r by multiplication, you could get rid of it by division……

Like this! C =2πr Divide both sides by 2π: 2π 2π This leaves you with the following: C = r 2π2π That’s it! That is all there is to it! Now r is by itself, and all of the other “stuff” is on the other side!

Here’s another one: Try solving the following formula for x: 5x + y = x 5x + y = x

Follow these steps to get x: 5x + y = x 1. Move your x’s together, to the same side: Which one should you move? The 5x or the x??? 5x + y = x 5x + y = x - 5x -5x - 5x -5x (you should move the 5x because it needs to be with the x on the other side, and it needs to be away from the y!

Steps 2 & 3: Now your equation should look like this! y = -4x y = -4x 2. What would be the next thing you should do to get the x by itself? (If you said DIVIDE BY – 4, THEN YOU’RE RIGHT!) y = -4x y = -4x Your answer will be y = x -4 -4

How ‘bout another one?!? Solve 6 – ay = 4(a – b) for a

Just follow the steps you have been using in other types of equations! 6 – ay = 4(a – b) Distributive property: 6 – ay = 4a – 4b Get the things with an “a” together, and the things that don’t have an “a” together: 6 – ay = 4a – 4b - 4a - 4a Simplify to get: 6 – ay – 4a = - 4b

Big Finish: 6 – ay – 4a = - 4b Simplify to get: - ay – 4a = - 4b – 6 Now, here’s the tricky part: You have two things on the left that have a’s and you can’t combine them because they aren’t like terms! You have to do something called Factoring: it goes like this: Ask yourself what a is being multiplied by in the two terms on the left: there is an a with – y, and an a with – 4, so you group them in parentheses:

Factor: - ay – 4a = - 4b – 6 Now looks like this: a(- y – 4) = - 4b – 6 (Its like the distributive property, backwards!) To get the a by itself, divide both sides by the stuff in the parentheses: a(- y – 4) = - 4b – 6 (- y – 4) (- y – 4) Your answer looks REALLY WEIRD!, but that’s OK!

Your answer should look like this: a= - 4b – 6 - y – 4 (you don’t have to keep the () on bottom any more) How’s that for fun!?!

Try one more : (if your brain is not already fried!) The perimeter of a square field is given by the equation P = 2l + 2w, where P represents the perimeter, l represents the length of the field, and w represents the width of the field. Solve the formula for l.

What should you do first?

Answer: P = 2l + 2w - 2w - 2w P - 2w = 2l 2 2 P - 2w = l 2

OMG!!!! Yes, these are hard! Yes, these are hard! Yes, you have to do them! Yes, you have to do them! Yes, you have an assignment! Yes, you have an assignment! Book page – 26 even Book page – 26 even (13 problems) (13 problems)

You’ll thank me one day…….