Are 4(2n - 1) - 3n and 5n - 4 equivalent Step by Step

Step by step

The question

Question: are 4(2n − 1) − 3n and 5n − 4 equivalent?

4(2n − 1) − 3n and 5n − 4

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

equivalent = equal for every number

First we simplify the first one: 4(2n − 1) − 3n.

We write it shorter, with the same value.

= 4(2n − 1) − 3n

1 Open the brackets

The 4 in front of the bracket multiplies every part inside.

a(b + c) = ab + ac

So we write 4 times each part.

= 4(2n) + 4(−1) − 3n

− × + = −

Watch the signs.

4 times 2n is 8n.

4 times (−1) is −4.

= 8n − 4 − 3n

2 Group like terms

Terms are the parts between the + and − signs.

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

All the n 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.

= 8n − 3n − 4

8n − 3n is 5n.

It is like 8 apples take away 3 apples: that is 5 apples.

8n − 3n = 5n

So the expression is 5n − 4.

= 5n − 4

3 Compare

Now both are 5n − 4.

The same terms.

= 5n − 4 = 5n − 4

So yes: they are equivalent.

= yes: equivalent

4 Check

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

The first gives 6.

The second gives 6.

The same.

So the answer is right!

n = 2: 4(2(2) − 1) − 3(2) = 6, 5(2) − 4 = 6

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.

Answer