# Honors Geometry Companion Book, Volume 1

2.2.1 Algebraic Proof − Worksheet

Example 1: Solve each equation. Write a justification for each step. 1. y + 1 = 5

2. t − 3.2 = − 8.3

+ x 3 2 −

3. 2 p − 30 = − 4 p + 6

4.

8

=

1 2

3 4

5.

6. 0 = 2( r − 3) + 4

= n

Example 2: 7. Amy’s favorite breakfast cereal has 102 Calories per serving. The equation C = 9 f + 90 relates the grams of fat f in one serving to the Calories C in one serving. How many grams of fat are in one serving of the cereal? Solve the equation for f and justify each step.

8. The equation C = \$5.75 + \$0.89 m relates the number of movie rentals m to the monthly cost C of a movie club membership. How many movies did Elias rent this month if his membership cost \$11.98? Solve the equation for m and justify each step.

Example 3: Write a justification for each step. 9. C 5 y + 6 2 y + 21

10.

9 n – 5

3 n

25

P

Q

R

AB = BC 5 y + 6 = 2 y + 21 3 y + 6 = 21 3 y = 15 y = 5 A B

PQ + QR = PR 3 n + 25 = 9 n − 5 25 = 6 n − 5 30 = 6 n 5 = n

105

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