Which of the following is equivalent to 3(2x - 5) + 4x? A) 2x

Step by step

The question

Question: simplify 3(2x − 5) + 4x.

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

3(2x − 5) + 4x

There are four choices.

First we solve it, the normal way.

Then we pick.

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(2x) + 3(−5) + 4x

− × + = −

Watch the signs.

3 times 2x is 6x.

3 times (−5) is −15.

= 6x − 15 + 4x

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.

= 6x + 4x − 15

6x + 4x is 10x.

It is like 6 apples plus 4 apples: that is 10 apples.

6x + 4x = 10x

So the expression is 10x − 15.

= 10x − 15

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.

Question: 3 × (2 × 2 − 5) + 4 × 2

= 3 × (−1) + 8 = −3 + 8 = 5

Now into our answer.

Answer: 10 × 2 − 15 = 20 − 15 = 5

Both give 5.

Same value, so 10x − 15 is right!

Both give 5

4 Pick the choice

Our answer is 10x − 15.

That is choice C.

C) 10x − 15

5 Why not the others

A is 2x − 15.

Wrong: 6x − 15 − 4x: took 4x away.

A) 2x − 15 ✗ 6x − 15 − 4x: took 4x away

B is 6x − 11.

Wrong: 6x − 15 + 4: added 4 to the number.

B) 6x − 11 ✗ 6x − 15 + 4: added 4 to the number

D is 10x − 5.

Wrong: 3 × (−5) is −15, not −5.

D) 10x − 5 ✗ 3 × (−5) is −15, not −5

Let's look back.

First: open the brackets.

Then: group like terms.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer