Solving Equations And Formulas
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Solving Equations And Formulas

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solving multivariable equations for a specific variable (algebra 1)

solving multivariable equations for a specific variable (algebra 1)

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Solving Equations And Formulas Presentation Transcript

  • 1. Solving Equations and Formulas Chapter 3 section 8
  • 2. Solving for a specific Variable
    • Sometimes equations involve multiple variables, or letters that stand for specific things, such as scientific formulas and physics equations
  • 3. Geometry Formulas:
    • The formula for Circumference of a circle is:
    • C =2 πr (2 x pi x radius)
    • We can solve the formula for r: (this means get r by itself!)
  • 4. What do you think we could do?
    • If the equation is set up as C = 2 π r, 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 2 π is “stuck” to r by multiplication, you could get rid of it by division……
  • 5. Like this!
    • C = 2 π r
    • Divide both sides by 2 π: 2 π 2 π
    • This leaves you with the following:
    • C = r
    • 2 π
    • 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!
  • 6. Here’s another one:
    • Try solving the following formula for x:
    • 5x + y = x
  • 7. Follow these steps to get x:
    • 5x + y = x
    • Move your x’s together, to the same side: Which one should you move? The 5x or the x???
    • 5x + y = x
    • - 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!
  • 8. Steps 2 & 3:
    • Now your equation should look like this!
    • 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
    • -4 -4
    • 3. Your answer will be y = x
    • -4
  • 9. How ‘bout another one?!?
    • Solve 6 – ay = 4( a – b ) for a
  • 10. Just follow the steps you have been using in other types of equations!
    • 6 – ay = 4( a – b )
    • Distributive property:
    • 6 – ay = 4 a – 4 b
    • Get the things with an “a” together, and the things that don’t have an “a” together:
    • 6 – ay = 4 a – 4 b
    • - 4a - 4a
    • Simplify to get:
    • 6 – ay – 4a = - 4b
  • 11. 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:
  • 12. 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!
  • 13. 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!?!
  • 14. Try one more : (if your brain is not already fried!)
    • The perimeter of a square field is given by the equation P = 2 l + 2 w , 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 .
  • 15. What should you do first?
  • 16. Answer:
    • P = 2 l + 2 w
    • - 2w - 2w
    • P - 2w = 2l
    • 2 2
    • P - 2w = l
    • 2
  • 17. OMG!!!!
    • Yes, these are hard!
    • Yes, you have to do them!
    • Yes, you have an assignment!
    • Book page 168 14 – 32 even
    • (10 problems)
  • 18. You’ll thank me one day…….
  • 19.