Question

Is 3x+12-2x equivalent to x +12? Use two properties of operations to justify your answer.

Answer 1

Yes, it is.

Explanation:

3x + 12 - 2x =

Use the commutative property of addition to change the order of the addition.

= 12 + 3x - 2x

Use the distributive property of addition over multiplication in reverse (which is factoring).

= 12 + x(3 - 2)

Do the operation: 3 - 2 = 1

= 12 + x * 1

Simplify x * 1 to just x.

= 12 + x

Use the commutative property of addition.

= x + 12

There you have x + 12 from 3x + 12 - 2x by using properties and operations.

Answer 2

Yes, x + 12

Explanation:

Simplify the following:

3 x - 2 x + 12

Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:

(3 x - 2 x) + 12

3 x - 2 x = x:

Answer: x + 12