Are 4x + 3 + 2x and 6x + 3 equivalent

Step by step

The question

Question: are 4x + 3 + 2x and 6x + 3 equivalent?

Equivalent means: the two are equal, whatever number the letter is.

First we simplify the first one: 4x + 3 + 2x.

We write it shorter, with the same value.

1 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

Each colour is one kind.

We move like terms next to each other.

Each term takes its sign with it.

4x + 2x is 6x.

It is like 4 apples plus 2 apples: that is 6 apples.

So the expression is 6x + 3.

2 Compare

Now both are 6x + 3.

The same terms.

So yes: they are equivalent.

3 Check

Let's check with a number: x = 2.

The first gives 15.

The second gives 15.

The same.

So the answer is right!

Let's look back.

First: group like terms.

Then: compare.

Last: check.