Are 8 - 3(x + 1) and 5 - 3x equivalent Step by Step

Step by step

The question

Question: are 8 − 3(x + 1) and 5 − 3x equivalent?

8 − 3(x + 1) and 5 − 3x

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

equivalent = equal for every number

First we simplify the first one: 8 − 3(x + 1).

We write it shorter, with the same value.

= 8 − 3(x + 1)

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.

= 8 + (−3)(x) + (−3)(1)

− × + = −

Watch the signs.

(−3) times x is −3x.

(−3) times 1 is −3.

= 8 − 3x − 3

2 Group like terms

Terms are the parts between the + and − signs.

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

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.

= −3x + 8 − 3

8 − 3 is 5.

8 − 3 = 5

So the expression is −3x + 5.

= −3x + 5

3 Compare

Now both are −3x + 5.

The same terms.

= −3x + 5 = −3x + 5

So yes: they are equivalent.

= yes: equivalent

4 Check

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

The first gives −1.

The second gives −1.

The same.

So the answer is right!

x = 2: 8 − 3(2 + 1) = −1, 5 − 3(2) = −1

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.

Answer