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Algebraic Proofs

This resource provides a structured approach to solving algebraic equations using proof statements and reasoning. It details various algebraic steps to simplify expressions and isolate variables, demonstrating how to manipulate equations effectively. Included are examples like solving for x in equations such as x + 5 = 19 and 5x + 5 = 40, utilizing properties like the Distributive Property and basic arithmetic operations. This guide serves as a valuable tool for students aiming to deepen their understanding of algebra.

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Algebraic Proofs

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  1. Algebraic Proofs

  2. Statement Reason • Given • - Prop. = • Simplify • X + 5 = 19 • - 5 - 5 • X = 14

  3. Statement Reason • Given • + Prop = • Simplify • 1 = x – 2 • +2 +2 • 3 = x

  4. Statement Reason • Given • x Prop. = • Simplify • x ÷ 7 = 6 • x 7 x 7 • x = 42

  5. Statement Reason • Given • - Prop = • Simplify • ÷ Prop = • Simplify • 5x + 4 = 39 • - 4 - 4 • 5x = 35 • ÷5 ÷5 • x = 7

  6. Statement Reason • Given • + Prop = • Simplify • ÷ Prop = • Simplify • 2x – 6 = 24 • + 6 + 6 • 2x = 30 • ÷2 ÷2 • x = 15

  7. Statement Reason • Given • Distributive Prop • + Prop = • Simplify • ÷ Prop = • Simplify • 7(4x – 10) = 14 • 28x – 70 = 14 • + 70 +70 • 28x = 84 • ÷28 ÷28 • x = 3

  8. Exit Slip Statement Reason • 5x + 5 = 40 • Given

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