1. § 2.3 The Multiplication Property of Equality

2. Martin-Gay, Beginning Algebra, 5ed 22 Multiplication Property of Equality If a, b, and c are real numbers, then a = b and ac = bc are equivalent equations Multiplication Property of Equality Example: – y = 8 y = – 8Simplify both sides. ( – 1)( – y) = 8( – 1) Multiply both sides by –1.

3. Martin-Gay, Beginning Algebra, 5ed 33 Example: Solving Equations Simplify both sides. Multiply both sides by 7.

4. Martin-Gay, Beginning Algebra, 5ed 44 Example: Solving Equations Simplify both sides. Multiply both sides by the fraction.

5. Martin-Gay, Beginning Algebra, 5ed 55 Divide both sides by 3. Example: Using Both Properties 3z – 1 = 26 3z = 27 Simplify both sides. z = 9 Simplify both sides. 3z – 1 + 1 = 26 + 1 Add 1 to both sides.

6. Martin-Gay, Beginning Algebra, 5ed 66 Example: Using Both Properties 12x + 30 + 8x – 6 = 10 20x + 24 = 10 Simplify the left side. 20x = – 14 Simplify both sides. Divide both sides by 20.Simplify both sides. 20x + 24 + ( – 24) = 10 + ( – 24) Add –24 to both sides.