1. The Multiplication Principle of Equality 2.3a 1.Solve linear equations using the multiplication principle. 2.Solve linear equations using both the addition and the multiplication principles.

2. Review 1 1 1 1 Multiplicative Inverses (Reciprocals) 6 1 6 1

3. Multiplication Principle of Equality The Multiplication Principle of Equality If a = b, then ac = bc for all real numbers a, b, and c, where c 0. Multiplying by ½ and dividing by 2 are equivalent!

4. Multiplication Principle of Equality  Multiply both sides of the equation by the multiplicative inverse of the coefficient or  Divide both sides by the coefficient. 1 1 1 2 1 1 1 2 If the coefficient is a fraction, multiply by the multiplicative inverse (reciprocal). If the coefficient is an integer, divide.

5. Multiplication Principle of Equality 1 1 1 1 1 -3 1 1

6. Addition and Multiplication Principle of Equality To Solve Linear Equations 1. Simplify both sides of the equation as needed. a. Distribute to clear parentheses. b. Combine like terms. 2. Use the addition principle so that all variable terms are on one side of the equation. 3. Use the addition principle so that all constants are on the other side. 4. Use the multiplication principle to isolate the variable. Use the addition principle BEFORE the multiplication principle!!!

7. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Check:

8. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Check:

9. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Check:

10. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Check:

11. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Check

12. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Contradiction Solution: No solution or

13. Addition and Multiplication Principle of Equality 1. Simplify 2. Move the variable terms. 3. Move the constants. 4. Isolate the variable. Identity Solution: All Real Numbers

14. Solve. 8m + 6 = 3(12 + 2m) a) 3 b) 5 c) 8 d) 15 2.3

15. Solve. 8m + 6 = 3(12 + 2m) a) 3 b) 5 c) 8 d) 15 2.3

16. Addition and Multiplication Principle of Equality Multiply by 3. Add 2. Solving is the same as “undoing” or reversing each operation. Divide by 3. Subtract 2.