Solving Equations And Formulas

19
Solving Equations and Solving Equations and Formulas Formulas Chapter 3 section 8 Chapter 3 section 8
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solving multivariable equations for a specific variable (algebra 1)

Transcript of Solving Equations And Formulas

Page 1: Solving Equations And Formulas

Solving Equations Solving Equations and Formulasand Formulas

Chapter 3 section 8Chapter 3 section 8

Page 2: Solving Equations And Formulas

Solving for a specific Solving for a specific VariableVariable

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

Page 3: Solving Equations And Formulas

Geometry Formulas:Geometry Formulas:

The formula for The formula for Circumference of a Circumference of a circle is:circle is:

C=2πr (2 x pi x radius)

We can solve the formula for r: (this means get r by itself!)

Page 4: Solving Equations And Formulas

What do you think we could What do you think we could do?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……

Page 5: Solving Equations And Formulas

Like this!Like this!

C =2πr Divide both sides by 2π: 2π 2π This leaves you with the following:

C = r2π

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!

Page 6: Solving Equations And Formulas

Here’s another one:Here’s another one:

Try solving the following formula for x:Try solving the following formula for x:

5x + y = x5x + y = x

Page 7: Solving Equations And Formulas

Follow these steps to get Follow these steps to get x:x:

5x + y = x5x + y = x1.1. Move your x’s together, to the same side: Move your x’s together, to the same side:

Which one should you move? The 5x or the x???Which one should you move? The 5x or the x???

5x + y = x5x + y = x - 5x -5x- 5x -5x

(you should move the 5x because it needs to be with (you should move the 5x because it needs to be with the x on the other side, and it needs to be away the x on the other side, and it needs to be away from the y!from the y!

Page 8: Solving Equations And Formulas

Steps 2 & 3:Steps 2 & 3:

Now your equation should look like this!Now your equation should look like this!

y = -4xy = -4x

2. What would be the next thing you should do to get the x by 2. What would be the next thing you should do to get the x by itself? itself?

(If you said DIVIDE BY – 4, THEN YOU’RE RIGHT!)(If you said DIVIDE BY – 4, THEN YOU’RE RIGHT!)

yy = = -4x-4x-4 -4-4 -4

3. Your answer will be 3. Your answer will be yy = x = x -4-4

Page 9: Solving Equations And Formulas

How ‘bout How ‘bout another one?!?another one?!?

Solve 6 – ay = 4(a – b) for a

Page 10: Solving Equations And Formulas

Just follow the steps you have Just follow the steps you have been using in other types of been using in other types of

equations!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

Page 11: Solving Equations And Formulas

Big Finish:Big Finish:

6 – ay – 4a = - 4b -6 -6 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:

Page 12: Solving Equations And Formulas

Factor:Factor:

- ay – 4a = - 4b – 6Now 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!

Page 13: Solving Equations And Formulas

Your answer should look like this: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!?!

Page 14: Solving Equations And Formulas

Try one more :Try one more :(if your brain is not already (if your brain is not already

fried!)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.

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What should you do first?What should you do first?

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

P - 2w = 2l 2 2 P - 2w = l 2

Page 17: Solving Equations And Formulas

OMG!!!!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 Yes, you have an

assignment!assignment! Book page 168 14 – 32 evenBook page 168 14 – 32 even

(10 problems)(10 problems)

Page 18: Solving Equations And Formulas

You’ll thank me one You’ll thank me one day…….day…….

Page 19: Solving Equations And Formulas