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Solving literal equations (formulas) for a specified variable.

Section 3.8. Solving literal equations (formulas) for a specified variable. SEPT. 7, 2009. Solve for Variables If you are given an equation with several variables in it, sometimes you may want to solve for just ONE of it’s variables. For example, for cube volume

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Solving literal equations (formulas) for a specified variable.

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  1. Section 3.8 Solving literal equations (formulas) for a specified variable. SEPT. 7, 2009

  2. Solve for Variables If you are given an equation with several variables in it, sometimes you may want to solve for just ONE of it’s variables. For example, for cube volume If you know the volume, width and height of the cube but not the length you want to use a more useful equation:

  3. We get from to by using the properties of equality to isolate the variable we want, L, on one side of the equation. Remember, when we put variables together we are multiplying, so To get Lon it’s own, divide by w and h so that on the left w and h cancel & you’re left with

  4. Answer Now 1) Solve 2x - 4y = 7 for xTo get x by itself, what is the first step? • Add 2x • Subtract 2x • Add 4y • Subtract 4y

  5. Ask yourself, What is the first thing we are doing to x? What is the second thing? 1) Solve 2x - 4y = 7 for xUse a DO-UNDO chart to help determine the steps DO UNDO · 2 -4y Follow the steps in the ‘undo’ column to isolate the variable. +4y ÷ 2 Complete the undo column by writing the opposite operations in opposite order.

  6. D U 1) Solve 2x - 4y = 7 for x · 2 -4y +4y ÷ 2 + 4y + 4y 2x = 7 + 4y 2 2 • Draw “the river” • Add 4y to both sides • Simplify • Divide both sides by 2 • Does it simplify? This fraction cannot be simplified because both terms in the numerator are not divisible by 2.

  7. Answer Now 2) Solve 2x - 4y = 7 for yTo get y by itself, what is the first step? • Add 2x • Subtract 2x • Add 4y • Subtract 4y

  8. D U 2) Solve 2x - 4y = 7 for y · -4 +2x -2x ÷ -4 - 2x - 2x -4y = 7 - 2x -4 -4 • Draw “the river” • Subtract 2x from both sides • Simplify • Divide both sides by -4 • Does it simplify? Nope!

  9. Answer Now 3) Solve for y.What is the first step? • Multiply by 3 • Divide by 3 • Add a • Subtract a

  10. D U 3) Solve for y: + a ÷ 3 · 3 - a • Draw “the river” • Clear the fraction – multiply both sides by 3 • Simplify • Subtract a from both sides • Simplify y + a = 3c -a -a y = 3c - a

  11. Answer Now 4) Solve for y: 4x – 2y = 12 • -4x + 12 • 4x - 12 • -2x + 6 • 2x - 6

  12. D U 4) Solve for y: 4x – 2y = 12 · -2 + 4x - 4x ÷ -2 - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x or y = 2x - 6 • Draw “the river” • Subtract 4x from both sides • Simplify • Divide both sides by -2 • Does it simplify? Yes!

  13. Answer Now 5) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L? • L = V - WH

  14. Answer Now 6) The formula for the volume of a pyramid is V = . Which equation solves the formula for h? • h = 3Vb

  15. HOMEWORK: PRACTICE WORKBOOK 3.8 #1-4 AND 17-20

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