Worked examples
The question
Question: are 3(x + 2) and 3x + 6 equivalent?
3(x + 2) and 3x + 6
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 3(x + 2).
We write it shorter, with the same value.
= 3(x + 2)
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(x) + 3(2)
3 times x is 3x.
3 times 2 is 6.
= 3x + 6
2 Compare
Now both are 3x + 6.
The same terms.
= 3x + 6 = 3x + 6
So yes: they are equivalent.
= yes: equivalent
3 Check
Let's check with a number: x = 2.
The first gives 12.
The second gives 12.
The same.
So the answer is right!
x = 2: 3(2 + 2) = 12, 3(2) + 6 = 12
Let's look back.
First: open the brackets.
Then: compare.
Last: check.
▶ Watch it solved
The question
Question: are 5(x − 1) + 2 and 5x − 3 equivalent?
5(x − 1) + 2 and 5x − 3
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 5(x − 1) + 2.
We write it shorter, with the same value.
= 5(x − 1) + 2
1 Open the brackets
The 5 in front of the bracket multiplies every part inside.
a(b + c) = ab + ac
So we write 5 times each part.
= 5(x) + 5(−1) + 2
− × + = −
Watch the signs.
5 times x is 5x.
5 times (−1) is −5.
= 5x − 5 + 2
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
−5 + 2 is −3.
−5 + 2 = −3
So the expression is 5x − 3.
= 5x − 3
3 Compare
Now both are 5x − 3.
The same terms.
= 5x − 3 = 5x − 3
So yes: they are equivalent.
= yes: equivalent
4 Check
Let's check with a number: x = 2.
The first gives 7.
The second gives 7.
The same.
So the answer is right!
x = 2: 5(2 − 1) + 2 = 7, 5(2) − 3 = 7
Let's look back.
First: open the brackets.
Then: group like terms.
Then: compare.
Last: check.
▶ Watch it solved
The question
Question: are 2(x + 3) + 3(x − 1) and 5x + 3 equivalent?
2(x + 3) + 3(x − 1) and 5x + 3
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 2(x + 3) + 3(x − 1).
We write it shorter, with the same value.
= 2(x + 3) + 3(x − 1)
1 Open the brackets
What is in front of a bracket multiplies every part inside.
a(b + c) = ab + ac
So we write each part times what is in front.
= 2(x) + 2(3) + 3(x) + 3(−1)
− × + = −
Watch the signs.
2 times x is 2x.
2 times 3 is 6.
3 times x is 3x.
3 times (−1) is −3.
= 2x + 6 + 3x − 3
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.
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.
= 2x + 3x + 6 − 3
2x + 3x is 5x.
It is like 2 apples plus 3 apples: that is 5 apples.
6 − 3 is 3.
2x + 3x = 5x
6 − 3 = 3
So the expression is 5x + 3.
= 5x + 3
3 Compare
Now both are 5x + 3.
The same terms.
= 5x + 3 = 5x + 3
So yes: they are equivalent.
= yes: equivalent
4 Check
Let's check with a number: x = 2.
The first gives 13.
The second gives 13.
The same.
So the answer is right!
x = 2: 2(2 + 3) + 3(2 − 1) = 13, 5(2) + 3 = 13
Let's look back.
First: open the brackets.
Then: group like terms.
Then: compare.
Last: check.
▶ Watch it solved
