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. 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. Do ·3 +2 Undo -2 ÷3

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 cm 3. Find its density. Givens: m = 16 g v = 8 cm 3 d = ? Formula: d = m / v Replace formula with givens: d = 16 g / 8 cm 3 Answer (with proper units): d = 2 g/cm 3

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 cm 3 and density of 2 g/cm 3. Find its mass. Givens: d = 2 g/cm 3 v = 8 cm 3 m = ? Formula: d = m / v but this is not the formula you need. Use Do/Undo method to develop a formula to isolate m DoUndo m = d · v ÷ v· v Replace formula with givens: m = 2 g/cm 3 · 8 cm 3 Answer (with proper units): m = 16 g

10. Practice Problems 1.What is the mass of a frictionless sled that is accelerating at 3 meters per second squared with a force of 130 N? (Use F = m · a) 2.What is the acceleration of a 1000 kg car pulled by a cable with 2000 N of force? (N = kg·m/s 2 ) 3.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