Solving Equations and Formulas Chapter 2 section 6.

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Presentation transcript:

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……

Example 1 - 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!

Ex. 2 Here’s another one: Try solving the following formula for y: 12x + 3y = 6 12x + 3y = 6

Follow these steps to get y: 12x + 3y = 6 1. Move your x’s to the right side of the equal sign 12x +3y = 6 12x +3y = x -12x - 12x -12x 3y = -12x + 6 3y = -12x x and 6 are not like terms so you can’t combine them.

Steps 2 & 3: Now your equation should look like this! 3y = -12x + 6 3y = -12x What would be the next thing you should do to get the y by itself? (If you said DIVIDE BY 3, THEN YOU ARE RIGHT!) 3Y = -12x Y = -12x Your answer will be y = -4x + 2

Ex. 3 How ‘bout another one?!? Solve 6 – ay = 4(a – b) for the variable in red

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 “b” alone on one side of the equal sign 6 – ay = 4a – 4b - 4a - 4a Simplify to get: 6 – ay – 4a = - 4b

Big Finish: 6 – ay – 4a = - 4b – ay – 4a = b -4 Divide both sides by -4 to solve for b

Ex. 4 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…….