1. Chapter 3 Unit Question How do we solve equations in algebra?

2. Open Learning Logs Date on Left…Section 3 – 3 on right

3. Warm Up Explain how to determine the sign of a sum of two numbers. Pass Learning Logs to the Back

4. Section 3 How do we use properties of addition to simplify or solve equations or expressions?

5. Homework Check Homework Check

6. Additive Identity Property a + 0 = a or 0 + a = a Examples: 1 + 0 = 1 0 + 5 = 5

7. Property of Opposites: a + (-a) = 0 or (-a) + a = 0 Examples: (-9) + 9 = 0 3 + (-3) = 0 In words, any number plus its opposite equals zero Also called additive inverse

8. Property of Opposites… The OpOp Property -(-a) = a Example: -(-5) = 5

9. Additive Property of Equality… If m = n, then m + c = n + c For all Real numbers m, n, and c Example: Let m = 4 n = 4 c = 6 m = nYou bet! 4 = 4No doubt! 4 + 6 = 4 + 6 10 = 10

10. Evaluate… -6.8 + 3 2.5 + (-7.5) PEMDAS !!!! - 6.8 - 6.8 + 7.5 + (-7.5)

11. Evaluate… 4

12. What is… The opposite of 8.2? a + b + -a The opposite of the opposite of 8.2?

13. We can use the Additive Property of Equality to solve equations! Example: b + 13 = 39 I choose that number to be -13 and I’ll add STRAIGHT DOWN If we assume this is true then We need to find a number to ADD both sides by to get b all by itself. -13 b+ 0= 26 b = 26

14. More use of the Additive Property of Equality to solve equations! Example: v + 20 = 14 I choose that number to be -20 and I’ll add STRAIGHT DOWN If we assume this is true then We need to find a number to add both sides by to get v all by itself. -20 v+ 0= -6 v = -6

15. So…the trick is coming up with a something to add to both sides of an equation. To solve a + x = b for x, add the opposite of a to both sides of the equation! AND THAT TRICK IS… Little rhythm to help you out… Drop the Op left and right, Draw the line and add

16. More examples… -5 + m = 12 What is being added to the variable? Drop the Op left and right, Draw the line and add +5 0 + m = 17 m = 17

17. More examples… v + (-18) = -15 What is being added to the variable? Drop the Op left and right, Draw the line and add +18 v + 0 = 3 v = 3 v + (-12) + (-6) = -15

18. Write and solve an equation… I have ¼ pound of butter. A recipe calls for ¾ pound. How much more butter do I need? ¼ + b = ¾ Let b = amount of butter needed - ¼ 0 + b = ½ So…I need ½ pound of butter b = ½

19. Homework HoffmaSheet 3 – 4