1. GEOMETRY HELP Justify each step used to solve 5x – 12 = 32 + x for x. 1.5x = 44 + xAddition Property of Equality 2.4x = 44Subtraction Property of Equality 3.x = 11Division Property of Equality Given: 5x – 12 = 32 + x Quick Check Reasoning in Algebra LESSON 2-4 Additional Examples

2. GEOMETRY HELP 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=21Simplify x=2Subtraction Property of Equality Reasoning in Algebra LESSON 2-4 Additional Examples Quick Check

3. GEOMETRY HELP Name the property that justifies each statement. 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. a.If x = y and y + 4 = 3x, then x + 4 = 3x. 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. Reasoning in Algebra LESSON 2-4 Additional Examples

4. GEOMETRY HELP (continued) c.If  P  Q,  Q  R, and  R  S, then  P  S. The property used is the Transitive Property of Congruence. 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 Quick Check