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Justify each step used to solve 5 x – 12 = 32 + x for x .

Reasoning in Algebra. LESSON 2-4. Additional Examples. Justify each step used to solve 5 x – 12 = 32 + x for x . Given : 5 x – 12 = 32 + x. 1. 5 x = 44 + x Addition Property of Equality 2. 4 x = 44 Subtraction Property of Equality 3. x = 11 Division Property of Equality.

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Justify each step used to solve 5 x – 12 = 32 + x for x .

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  1. Reasoning in Algebra LESSON 2-4 Additional Examples Justify each step used to solve 5x – 12 = 32 + x for x. Given: 5x – 12 = 32 + x 1. 5x = 44 + xAddition Property of Equality 2. 4x = 44 Subtraction Property of Equality 3.x = 11 Division Property of Equality Quick Check

  2. Reasoning in Algebra LESSON 2-4 Additional Examples Suppose that points A, B, and C are collinear with point B between points A and C. Solve for x if AB = 4 + 2x, BC = 15 – x, and AC = 21. Justify each step. AB + BC = ACSegment Addition Postulate (4 + 2x) + (15 – x) = 21Substitution Property of Equality 19 + x = 21 Simplify x = 2 Subtraction Property of Equality Quick Check

  3. Reasoning in Algebra LESSON 2-4 Additional Examples Name the property that justifies each statement. a. If x = y and y + 4 = 3x, then x + 4 = 3x. The conclusion of the conditional statement is the same as the equation y + 4 = 3x (given) after x has been substituted for y (given). The property used is the Substitution Property of Equality. b. If x + 4 = 3x, then 4 = 2x. The conclusion of the conditional statement shows the result after x is subtracted from each side of the equation in the hypothesis. The property used is the Subtraction Property of Equality.

  4. Use the Transitive Property of Congruence for the first two parts of the hypothesis: If PQ and QR, then PR. Use the Transitive Property of Congruence for PR and the third part of the hypothesis: If PR and RS, then PS. Reasoning in Algebra LESSON 2-4 Additional Examples (continued) c. If PQ, QR, and RS, then PS. The property used is the Transitive Property of Congruence. Quick Check

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