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

Step by step

The question

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

2(x + 3) + 3(x − 1) and 5x + 3

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

equivalent = equal for every number

First we simplify the first one: 2(x + 3) + 3(x − 1).

We write it shorter, with the same value.

= 2(x + 3) + 3(x − 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.

= 2(x) + 2(3) + 3(x) + 3(−1)

− × + = −

Watch the signs.

2 times x is 2x.

2 times 3 is 6.

3 times x is 3x.

3 times (−1) is −3.

= 2x + 6 + 3x − 3

2 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.

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.

= 2x + 3x + 6 − 3

2x + 3x is 5x.

It is like 2 apples plus 3 apples: that is 5 apples.

6 − 3 is 3.

2x + 3x = 5x

6 − 3 = 3

So the expression is 5x + 3.

= 5x + 3

3 Compare

Now both are 5x + 3.

The same terms.

= 5x + 3 = 5x + 3

So yes: they are equivalent.

= yes: equivalent

4 Check

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

The first gives 13.

The second gives 13.

The same.

So the answer is right!

x = 2: 2(2 + 3) + 3(2 − 1) = 13, 5(2) + 3 = 13

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.

Answer