Which expression is equivalent to 4(3x - 2) - 5x?

Step by step

The question

Question: which expression is equivalent to 4(3x − 2) − 5x?

Equivalent means: the same value for every x.

Simplify means: write it shorter, with the same value.

There are four choices.

First we simplify it, the normal way.

Then we pick.

1 Open the brackets

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

So we write 4 times each part.

Plus times minus is minus.

4 times 3x is 12x.

4 times (−2) is −8.

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.

We move like terms next to each other.

Each term takes its sign with it.

12x − 5x is 7x.

It is like 12 apples take away 5 apples: that is 7 apples.

So the expression is 7x − 8.

3 Check

Let's check.

We pick a small number for each letter: x = 2.

Any number works, and a small one keeps the sums easy.

We put it into the question.

Now into our answer.

Both give 6.

Same value, so 7x − 8 is right!

4 Pick the choice

Our answer is 7x − 8.

That is choice A.

5 Why not the others

B is 7x − 2.

Wrong: 4 × (−2) is −8, not −2.

C is 7x + 8.

Wrong: 4 × (−2) is −8, not +8.

D is 17x − 8.

Wrong: 12x + 5x: added instead of taking away.

Let's look back.

First: open the brackets.

Then: group like terms.

Then: check.

Then: pick the choice.

Last: why not the others.