Worksheet: Algebraic Proof: Solve Each Equation. Write A Reason For Every Step.

Name: WORKSHEET: Algebraic Proof Solve each equation. Write a reason for every step. 1. 4x = 12x + 32 2. 28 + 12x = 8x – 4 3. 60x + 153 = 9x + 51 4. -4x + 10 = -5x + 18 5. -3(x + 2) = 16 – x 6. -x – 2(9 – 8x) = 12 7. 6(x – 6) = x(16 – 7) 8. 1 4 x + 10 = 2 C o p yr ig ht © G le nc o e/ M cG ra w -H ill , a d iv is io n o f T he M cG ra w -H ill C o m p an ie s, In c. NAME DATE PERIOD Chapter 2 25 Glencoe Geometry State the property that justifies each statement. 1. If 80 = m∠A, then m∠A = 80. 2. If RS = TU and TU = YP, then RS = YP. 3. If 7x = 28, then x = 4. 4. If VR + TY = EN + TY, then VR = EN. 5. If m∠1 = 30 and m∠1 = m∠2, then m∠2 = 30. Complete the following proof. 6. Given: 8x - 5 = 2x + 1 Prove: x = 1 Proof: Write a two-column proof to verify the conjecture. 7. If −−− PQ  −−− QS and −−− QS  −− ST then PQ = ST. QP TS Skills Practice Algebraic Proof 2-6 Statements Reasons a. 8x - 5 = 2x + 1 b. 8x - 5 - 2x = 2x + 1 - 2x c. d. e. 6x = 6 f. 6x − 6 = 6 − 6 g. a. b. c. Substitution Property d. Addition Property e. f. g. 015_030_GEOHWPC02_890849.indd 25 6/26/08 3:03:38 PM C o p yr ig ht © G le nc o e/ M cG ra w -H ill , a d iv is io n o f T he M cG ra w -H ill C o m p an ie s, In c. NAME DATE PERIOD Chapter 2 25 Glencoe Geometry Algebraic Proof A list of algebraic steps to solve problems where each step is justified is called an algebraic proof, The table shows properties you have studied in algebra. The following properties are true for any real numbers a, b, and c. Addition Property of Equality If a = b, then a + c = b + c. Subtraction Property of Equality If a = b, the a - c = b - c. Multiplication Property of Equality If a = b, then a · c = b · c. Division Property of Equality If a = b and c ≠ 0, then, a − c = b − c . Reflexive Property of Equality a = a Symmetric Property of Equality If a = b and b = a. Transitive Property of Equality If a = b and b = c, then a = c. Substitution Property of Equality If a = b,then a may be replaced by b in any equation or expression. Distributive Property a (b + c) = ab + ac Solve 6x + 2(x - 1) = 30. Write a justification for each step. Algebraic Steps Properties 6x + 2(x - 1) = 30 Original equation or Given 6x + 2x - 2 = 30 Distributive Property 8x - 2 = 30 Substitution Property of Equality 8x - 2 + 2 = 30 + 2 Addition Property of Equality 8x = 32 Substitution Property of Equality 8x − 8 = 32 − 8 Division Property of Equality x = 4 Substitution Property of Equality Exercises Complete each proof. Study Guide and Intervention Algebraic Proof 2-6 Example 2. Given: 4x + 8 = x + 2 Prove: x = -2 Proof: Statements Reasons a. 4x + 8 = x + 2 a. b. 4x + 8 - x = b. x + 2 - x c. 3x + 8 = 2 c. Substitution d. d. Subtr. Prop. e. e. Substitution f. 3x − 3 = -6 − 3 f. g. g. Substitution 1. Given: 4x + 6 − 2 = 9 Prove: x = 3 Proof: Statements Reasons a. 4x + 6 − 2 = 9 a. b. – ( 4x + 6 − 2 ) = 2(9) b. Mult. Prop. c. 4x + 6 = 18 c. d. 4x + 6 - 6 = 18 - 6 d. e. 4x = e. Substitution f. 4x − 4 = f. Div. Prop. g. g. Substitution 015_030_GEOSGIC02_890848.indd 25 5/13/08 9:28:40 PM