Are 10 - 2(a - 4) and 18 - 2a equivalent Step by Step

Step by step

The question

Question: are 10 − 2(a − 4) and 18 − 2a equivalent?

10 − 2(a − 4) and 18 − 2a

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

equivalent = equal for every number

First we simplify the first one: 10 − 2(a − 4).

We write it shorter, with the same value.

= 10 − 2(a − 4)

1 Open the brackets

The (−2) in front of the bracket multiplies every part inside.

a(b + c) = ab + ac

So we write (−2) times each part.

= 10 + (−2)(a) + (−2)(−4)

− × − = +

Watch the signs.

(−2) times a is −2a.

(−2) times (−4) is 8.

= 10 − 2a + 8

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.

= −2a + 10 + 8

10 + 8 is 18.

10 + 8 = 18

So the expression is −2a + 18.

= −2a + 18

3 Compare

Now both are −2a + 18.

The same terms.

= −2a + 18 = −2a + 18

So yes: they are equivalent.

= yes: equivalent

4 Check

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

The first gives 14.

The second gives 14.

The same.

So the answer is right!

a = 2: 10 − 2(2 − 4) = 14, 18 − 2(2) = 14

Let's look back.

First: open the brackets.

Then: group like terms.

Then: compare.

Last: check.

Answer