Question

(01.07, 02.01 MC) Brian solved the following equation: 6(3x – 5) = 4(4x + 2) Step Work Justification 1 18x – 30 = 16x + 8 2 2x – 30 = 8 3 2x = 38 4 x = 19 Which of the following has all correct justifications Brian used to solve this equation? 1. Associative property of addition. 2. Subtraction property of equality. 3. Addition property of equality. 4. Multiplicative inverse. 1. Associative property of addition. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality. 1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality. 1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Multiplicative property of equality.

Answer 1

6(3x - 5) = 4(4x + 2) Given

(6)(3x) + (6)(-5) = (4)(4x) + (4)(2) Distributive property

18x - 30 = 16x + 8

18x - 16x - 30 = 16x - 16x + 8 Subtraction property of equality

2x - 30 = 8

2x - 30 + 30 = 8 + 30 Addition property of equality

2x = 38

2x : 2 = 38 : 2 Division property of equality

x = 19