What properties were used to prove that the expressions 7x + 4 - x - 2 and 6x + 2 are equivalent

Hello mate!

we have these two equations:

7x + 4 - x - 2

6x + 2

And we want to see which properties are needed to see if the expressions are equivalents.

Let's do it.

Start with the first equation:

7x + 4 - x - 2

Let's separate the terms with x and the therms without x, this is:

7x - x + 4 - 2

(7x - x) + (4 - 2)

x(7 -1) + (4 -2)

6x + 2

then 7x + 4 - x - 2  is equivalent to 6x + 2

Just doing that simplification, you can see that both equations are equivalent. The properties used are the commutative property of the addition ( to order the sum in the parentheses) and the distributive property of the multiplications, in order to take out the common factor x in the first parentheses)

Step-by-step explanation:

7x+4-x-2=6x+2 (Combine All alike terms)

6x+2=6x+2  (I mean that is all you really have to do but if it makes you go to more... then the next step would be Subtraction Property)

6x+2-2=6x+2-2 which is 6x=6x (This would be division Property )

Then it would be equal to each another completely leaving it 1x=1x

well there are two answers for that.

1: you need 120 ones then that will equal up to 120.

2: you could also do one 100 and 2 tens.

those are the answers that i have thought of.