Are 6(x + 3) - 4 and 6x + 14 equivalent

Step by step

The question

Question: are 6(x + 3) − 4 and 6x + 14 equivalent?

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

First we simplify the first one: 6(x + 3) − 4.

We write it shorter, with the same value.

1 Open the brackets

The 6 in front of the bracket multiplies every part inside.

So we write 6 times each part.

6 times x is 6x.

6 times 3 is 18.

2 Group like terms

Terms are the parts between the + and − signs.

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

Plain numbers go together.

Each colour is one kind.

18 − 4 is 14.

So the expression is 6x + 14.

3 Compare

Now both are 6x + 14.

The same terms.

So yes: they are equivalent.

4 Check

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

The first gives 26.

The second gives 26.

The same.

So the answer is right!

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.