Are 3(x + 2) + x and 4x + 2 equivalent Step by Step

Step by step

The question

Question: are 3(x + 2) + x and 4x + 2 equivalent?

3(x + 2) + x and 4x + 2

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

equivalent = equal for every number

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

We write it shorter, with the same value.

= 3(x + 2) + x

1 Open the brackets

The 3 in front of the bracket multiplies every part inside.

a(b + c) = ab + ac

So we write 3 times each part.

= 3(x) + 3(2) + x

3 times x is 3x.

3 times 2 is 6.

= 3x + 6 + x

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.

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.

= 3x + x + 6

3x + x is 4x.

It is like 3 apples plus 1 apple: that is 4 apples.

3x + x = 4x

So the expression is 4x + 6.

= 4x + 6

3 Compare

4x + 6 and 4x + 2 are not the same.

= 4x + 6 ≠ 4x + 2

So no: they are not equivalent.

= no: not equivalent

4 Check

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

The first gives 14.

The second gives 10.

Different.

So the answer is right!

x = 2: 3(2 + 2) + 2 = 14, 4(2) + 2 = 10

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.

Answer