1. Solving Linear Equations You already know how, but do you know why????

2. Solve this equation! 3x + 4 = 31

3. Why did you do what you did? Steps we took to solve the equation: Subtract 4 from both sides of the equation Divide by 3 on both sides of the equation

4. Properties of Equality Subtraction Property of Equality If a=b, then a-c=b-c Division Property of Equality If a=b and c  0, then a÷c=b÷c

5. Other Properties of Equality Reflexive Property of Equality a=a Symmetric Property of Equality If a=b, then b=a Transitive Property of Equality If a=b and b=c, then a=c Addition Property of Equality If a=b, then a+c=b+c Multiplication Property of Equality If a=b, then a  c=b  c Substitution Property of Equality If a=b, then b may be substituted for a in any expression containing a.

6. Two Column Proofs They allow us to provide justifications for our steps of solving equations in an organized and methodical manner. To justify our answer means to prove why what we did is correct and works.

7. Two Column Proofs STATEMENTJUSTIFICATION 3x + 4 = 31 ? 3x = 27 ? x = 9 ?

8. Now you try! Solve and Justify Using a Two Column Proof: 8x – 1 = 23 – 4x

9. Practice!! Think-Ink-Pair-Share With each of the next problems, think about how to solve it and the justifications that are needed. Create a two column proof for the problem. You will then pair up with your partner to check each other on the work you did. We will then get one person or pair to come up and show how they worked the problem to make sure everyone in the class gets it.

10. Practice Problems

11. Literal Equations An equation that has no numbers and only has variables. Examples: C=2  r A=  r 2 V=lwh

12. Solve the literal equation above for “l” V=lwh What inverse operations are needed to do this?

13. Solve the literal equation above for “r” A =  r 2 What inverse operations are needed to do this?

14. Real World Applications Ms. Rogers and Ms. Bradbury bought 25 total pencils to share with their classes. If Ms. Rogers bought 17, how many did Ms. Bradbury purchase?

15. Real World Applications Ms. Herrington bought 6 shirts for an unknown amount of money each. She also bought a pair of pants that cost her 30 dollars. If her entire purchase cost $60, how much did each of her shirts cost? (Don’t worry about tax here, because she was a smart shopper and went on tax free weekend!)

16. Homework

17. Summarizer Match the steps of solving an equation to the justifications for that step. Then answer the question below.