Question

What belongs in the box marked with the question mark in the proof?

Given: 3x - 4 = 2(x + 8), Prove: x = 20
Statement

Reason

(1) 3x - 4 = 2(x + 8)



(2) 3x - 4 = 2x + 16



(3) 3x = 2x + 20                                               (?)



(4) x = 20

Answer 1

(1) 3x - 4 = 2(x + 8) ..............Given
(2) 3x - 4 = 2x + 16...............Distributive property
(3) 3x = 2x + 20-----------------Addition property of equality
(4) x = 20-------------------------Subtraction property of equality

Answer 2

Subtraction

`3\cdot(x)-2\cdot(x)=20`

Explanation:

We can determine x=20 by solving x:

`3\cdot(x)-4=2\cdot(x+8)`

we multiply the terms in the brackets with 2:

`3\cdot(x)-4=2\cdot(x)+2\cdot(8)`

We then take the 2x to the right hand side

`3\cdot(x)-3\cdot(x)=20`

`x=20`