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Solving Literal Equations

Solving Literal Equations. Solving equations for different variables -Useful in Physics and Mathematics- Chapter 3 in Prentice Hall Algebra 1. Review. Solve: 3x + 2 = 8 - 2 -2 3x = 6 ÷3 ÷3 x = 2

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Solving Literal Equations

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  1. Solving Literal Equations Solving equations for different variables -Useful in Physics and Mathematics- Chapter 3 in Prentice Hall Algebra 1

  2. Review Solve: 3x + 2 = 8 - 2 -2 3x = 6 ÷3 ÷3 x = 2 At this level in our mathematics education, we should all be able to solve this equation. Let’s examine what is happening in more depth.

  3. Do ·3 +2 Undo -2 ÷3 3x + 2 = 8 • We are trying to isolate x, but what is preventing x from being by itself? Fill in the Do column, from closest to x to furthest from x. • Now, fill in the Undo column, by writing the opposite operations in the opposite order as the Do column. • To solve, we simply follow the directions of the Undo column from top to bottom.

  4. We can follow the same process as we solve literal equations. • Solve this common formula for r • r is not isolated, because t is multiplying it. Fill in the Do column. • Now, fill in the Undo column. What is the opposite operation of multiplying? • To solve for r, just follow the directions of the Undo column. Do ·t Undo ÷t

  5. ÷ t÷ t We have solved the equation for r, which means we have isolated r.

  6. Physics Application • Often, you will be given a formula such as F = m · a, where F is force, m is mass, and a is acceleration. • This works very nicely if you know mass and acceleration. You can replace m and a with your known quantities. • But what if you knew m and F but not a?

  7. When you are working with word problems, use this format to show your work and solve: Givens: Formula: (and solve for unknown) Replace formula with givens: Answer (with proper units):

  8. A 16 g marble is dropped in a cup of water. It has a volume of 8 cm3. Find its density. Givens: m = 16 g v =8 cm3 d = ? Formula: d = m / v Replace formula with givens: d = 16 g / 8 cm3 Answer (with proper units): d = 2 g/cm3

  9. But what if your formula is not solved for the variable in question? Example:A marble is dropped in a cup of water. It has a volume of 8 cm3 and density of 2 g/cm3. Find its mass. Givens: d = 2 g/cm3 v =8 cm3 m = ? Formula: d = m / v but this is not the formula you need. Use Do/Undo method to develop a formula to isolate m Do Undo m = d · v ÷ v · v Replace formula with givens: m = 2 g/cm3 ·8 cm3 Answer (with proper units): m = 16 g

  10. Practice Problems • What is the mass of a frictionless sled that is accelerating at 3 meters per second squared with a force of 130 N? (UseF = m · a) • What is the acceleration of a 1000 kg car pulled by a cable with 2000 N of force? (N = kg·m/s2) • How much force is exerted to do 2 J of work in moving a book 2 m? (W = f · d, Joules = N · m)

  11. Thanks to: • Henrico County Public Schools, Virginia

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