Question

Is 3a + 2b + 4a and 7a + 2b equivalent?

Answer 1

We are given two expressions:

1.) 3a+2b+4a

2.) 7a+2b

Let’s set them equal to each other to see if they are equivalent. If they are, they will look identical (equal) on both sides:

(3a+2b+4a)=(7a+2b)

Apply the commutative property of addition:

(3a+4a+2b)=(7a+2b)

Combine like terms:

7a+2b=7a+2b

Is this a true statement? Yes. Notice that both the left and right sides of the equation are identical. This is because they are indeed equal when simplified, and thus they ARE equivalent.

Answer 2

To determine if the expressions 3a + 2b + 4a and 7a + 2b are equivalent, we can simplify each expression and compare them.

First, let's simplify 3a + 2b + 4a:

Combine like terms:
3a + 4a + 2b = 7a + 2b

Now, let's compare this with 7a + 2b:

We can see that 7a + 2b is equal to 7a + 2b.

Therefore, the expressions 3a + 2b + 4a and 7a + 2b are equivalent.