1. Objective The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. Designed by D. R. High School Modified by T.Breland- Gaddis

2. A Variable Expression is a group of numbers, variables, and operations. (No equal sign) Examples 12m - 42 3x + 2

3. An Equation is a mathematical sentence that contains an equal sign (=). Examples 2 + 4 = 6 3x + 2 = 11

4. Expression, equation, or inequality? 13x + 14y = 30 1. Expression 2. Equation Answer Now

5. Expression, equation, or inequality? -2x - 4 1. Expression 2. Equation Answer Now

6. Expression, equation, or inequality? 10a - 22 = -92 1. Expression 2. Equation Answer Now

7. Sometimes you can solve an equation by applying the order of operations. 4 + 5 2 = m 8 - 1 2 = m 2 is the solution. It is a number that replaces the variable (m) and makes the equation true.

8. A set is a collection of objects or numbers. Each object in the set is called an element. Example Coins = {Penny, Nickel, Dime, Quarter, Half Dollar, Dollar} Coins is the set & Dime is an element of the set of Coins.

9. REMEMBER:An Equation is a mathematical sentence that contains an equal sign (=). Examples 2 + 4 = 6 3x + 2 = 11

10. Solving Equations

11. What it means to solve: To solve for x would mean to get x by itself on one side of the equation, with no x’s on the other side. (x = __ ) To solve for y would mean to get y by itself on one side of the equation, with no y’s on the other side. (y = __ )

12. Ask yourself, What is the first thing we are doing to x? What is the second thing? 1) Solve 2x - 4y = 7 for x Use 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.

13. 2) Solve 2x - 4y = 7 for y To get y by itself, what is the first step? 1. Add 2x 2. Subtract 2x 3. Add 4y 4. Subtract 4y Answer Now

14. 2) Solve 2x - 4y = 7 for y 1.Draw “the river” 2.Subtract 2x from both sides 3.Simplify 4.Divide both sides by -4 5.Does it simplify? D U · -4 +2x -2x ÷ -4 - 2x -4y = 7 - 2x -4 -4 Nope!

15. 4) Solve for y: 4x – 2y = 12 1.Draw “the river” 2.Subtract 4x from both sides 3.Simplify 4.Divide both sides by -2 5.Does it simplify? D U · -2 + 4x - 4x ÷ -2 - 4x -2y = 12 –4x -2 -2 y = -6 + 2x or y = 2x - 6 Yes!

16. 4) Solve for y: 4x – 2y = 12 1. -4x + 12 2. 4x - 12 3. -2x + 6 4. 2x - 6 Answer Now

17. Literal Equations

18. Equations with several variables (letters) are called literal equations. Your job, usually, will be to solve the equation for one of the variables. The letters that do not represent your desired variable move to the other side of the equal sign so that the one variable you are solving for stands alone.

19. Formulas are good examples of literal equations. A formula is an equation that states a rule for the relationship between certain quantities. Ex: A = lw What do A, l, and w stand for? Can you solve for “l”?

21. Identify the target variable. The first thing you need to do is identify what variable you are solving for, or your target variable. Your goal is to get all the letters in your equation on one side of the equation, and your target variable, by itself, on the other side of the equation.

22. Mind the order of operations. When solving literal equations, just like when solving linear equations, you need to use the order of operations.

23. Move the letters. Move all the letters to one side of the equation, leaving your target variable isolated.

24. Solve for the target variable. You are done when target variable is isolated. Keep in mind that due to all the variables, you will not be able to simplify your equations. When your target variable is isolated on one side of the equation, with all the other variables on the other side, you are done.

25. 1. L = V - WH 2. 3. 4. 5) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L? Answer Now

26. 1. h = 3Vb 2. 3. 4. 6) The formula for the volume of a pyramid is V =. Which equation solves the formula for h? Answer Now

27. Try a few on your own. Solve P = 1.2W for W. H 2 Solve P = 2l + 2w for l. Solve 4x - 3m = 2mx - 5 for x.

28. The answers: DO UNDO · 1.2 · H 2 ÷ H 2 ÷ 1.2 W = PH 2 1.2 DO UNDO · 2 -2w +2w ÷ 2 l = P - 2w 2 Subtract 2mx, then Add 3m to get 4x - 2mx = 3m - 5 x(4 - 2m) = 3m - 5 Divide by (4 - 2m) x = 3m - 5 4 - 2m