Question

Bradley solved the following equation: 4(5x – 6) = 2(8x + 10) Step Work Justification 1 20x – 24 = 16x + 20 2 4x – 24 = 20 3 4x = 44 4 x = 11 Which of the following has all correct justifications Bradley 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. Multiplicative property of equality. 1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality.

Answer 1

Solution:

The equation solved by Bradley is

→4(5x – 6) = 2(8x + 10)

Step Work  

1. 20 x – 24 = 16 x + 20    → [ Distributive property]

Taking variable on one side of equation

2 . 4 x – 24 = 20  → [Subtraction property of equality.]

Taking constant on one side of equation

3 . 4 x = 44 →[Addition property of equality.]

Dividing both sides by 4

4 . x = 11          → [Division property of equality.]

Out of all the four options given ,Fourth option [ 1. Distributive property. 2. Subtraction property of equality. 3. Addition property of equality. 4. Division property of equality ], completely satisfies the work done  in equation.