§ 2.3 The Multiplication Property of Equality. Martin-Gay, Beginning Algebra, 5ed 22 Multiplication Property of Equality If a, b, and c are real numbers,

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Presentation transcript:

§ 2.3 The Multiplication Property of Equality

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.

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

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

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 – = Add 1 to both sides.

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