Are 5(m + 2) - 2(m + 1) and 3m + 8 equivalent Step by Step

Step by step

The question

Question: are 5(m + 2) − 2(m + 1) and 3m + 8 equivalent?

5(m + 2) − 2(m + 1) and 3m + 8

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

equivalent = equal for every number

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

We write it shorter, with the same value.

= 5(m + 2) − 2(m + 1)

1 Open the brackets

What is in front of a bracket multiplies every part inside.

a(b + c) = ab + ac

So we write each part times what is in front.

= 5(m) + 5(2) + (−2)(m) + (−2)(1)

− × + = −

Watch the signs.

5 times m is 5m.

5 times 2 is 10.

(−2) times m is −2m.

(−2) times 1 is −2.

= 5m + 10 − 2m − 2

2 Group like terms

Terms are the parts between the + and − signs.

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

All the m terms go together.

Plain numbers go together.

Each colour is one kind.

like terms = same letters,

same powers

We move like terms next to each other.

Each term takes its sign with it.

= 5m − 2m + 10 − 2

5m − 2m is 3m.

It is like 5 apples take away 2 apples: that is 3 apples.

10 − 2 is 8.

5m − 2m = 3m

10 − 2 = 8

So the expression is 3m + 8.

= 3m + 8

3 Compare

Now both are 3m + 8.

The same terms.

= 3m + 8 = 3m + 8

So yes: they are equivalent.

= yes: equivalent

4 Check

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

The first gives 14.

The second gives 14.

The same.

So the answer is right!

m = 2: 5(2 + 2) − 2(2 + 1) = 14, 3(2) + 8 = 14

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.

Answer