Are 5(x - 1) + 2 and 5x - 3 equivalent

Step by step

The question

Question: are 5(x − 1) + 2 and 5x − 3 equivalent?

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

First we simplify the first one: 5(x − 1) + 2.

We write it shorter, with the same value.

1 Open the brackets

The 5 in front of the bracket multiplies every part inside.

So we write 5 times each part.

Watch the signs.

5 times x is 5x.

5 times (−1) is −5.

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.

−5 + 2 is −3.

So the expression is 5x − 3.

3 Compare

Now both are 5x − 3.

The same terms.

So yes: they are equivalent.

4 Check

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

The first gives 7.

The second gives 7.

The same.

So the answer is right!

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.