Question

explain how the distributive property and the commutative property of addition are used to the example to show that 2(x+1)+2x is equivalent to 4x + 2

Answer 1

Distributive property:

$a(b+c)=ab+ac$

Commutative property:

$x+y=y+x$

So, using the previous properties:

$\begin{gathered} 2(x+1)+2x=2\cdot x+2\cdot1+2x \\ \text{add like terms:} \\ (2x+2x)+2 \\ 4x+2\equiv4x+2 \end{gathered}$