1. 1-4: Properties of Equality and Algebraic Proofs Unit 1: Functions English Casbarro

2. You have solved equations and inequalities for some time now. You must justify your steps for solving the problems now.  Addition/Subtraction Property of Equality  If a = b, then a + c = b + c  If a = b, then a – c = b – c  Multiplication/Division Property of Equality  If a = b, then ac = bc  If a = b, then

3. More Properties of Equality  Distributive Property  a(b + c) = ab + ac  Substitution Property  If a = b, then b can be substituted for a in any expression or equation  Reflexive Property  If a is a real number, then a = a.  Symmetric Property  If a = b, then b = a.  Transitive Property  If a = b, and b = c, then a = c.

4. Given: 3x + 12 = 8x – 18 Prove: x = 6 StatementsReasons 1. 3x + 12 = 8x – 181. 2. 12 = 5x – 182. 3. 30 = 5x3. 4. 6 = x4. 5. x = 65.

5. Given: 3x + 5 = 17 Prove: x = 4 StatementsReasons 1. 3x + 5 = 171. 2. 3x = 122. 3. x = 43.

6. Given: – 6x – 5 = –95 Prove: x = 15 StatementsReasons 1. 2. 3.

7. Given: 3(5x + 1) = 13x + 5 Prove: x = 1 StatementsReasons 1. 2. 3. 4. 5.

8. Segment Addition Postulate So, the parts of the segment add up to the whole segment.

9. This is just another way of creating equations for you to prove! StatementsReasons 1. 2. 3. 4. 5.

10. In the picture, JL = 120. Find JK and KL And justify each of your steps. StatementsReasons 1. 2. 3. 4. 5.

11. Angle Addition Postulate So, the parts of the angle add up to the whole angle.

12. This is just another way of creating equations for you to prove! StatementsReasons 1. 2. 3. 4. 5.

13. StatementsReasons 1. 2. 3. 4. 5.