Worked examples
The question
Question: if 3x + 6 = 21, what is x + 2?
3x + 6 = 21
We want x + 2.
Let's look for it inside the equation.
x + 2 = ?
1 Compare the two
Look at 3x + 6 and x + 2.
We compare them part by part.
3x is 3 times x.
3x = 3 × x
6 divided by 2 is 3.
So 6 is 3 times 2.
6 ÷ 2 = 3, so 6 = 3 × 2
Every part of 3x + 6 is 3 times a part of x + 2.
2 Take out the 3
So we can write each part as 3 times.
3 × x + 3 × 2 = 21
3 times each part is the same as 3 times the whole bracket: 3(x + 2).
Opening the bracket gives 3x + 6 back.
3(x + 2) = 21
3 Remove the 3
3(x + 2) means 3 times the bracket.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3(x + 2)3 = 213
3 divided by 3 is 1.
So just the bracket is left.
21 divided by 3 is 7.
213 = 7
So x + 2 = 7!
x + 2 = 7
Careful!
Many people find x and stop.
But the question asks for x + 2.
Careful: the question asks for x + 2, not x
4 Check
Let's check the long way: first we find x.
3x + 6 = 21
We want x by itself.
Two things are stuck to x: times 3 and + 6.
First x was times 3.
Then + 6.
To take them off, we go backwards.
First we remove the + 6.
Then the times 3.
x → × 3 → + 6
take off: − 6, then ÷ 3
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
3x + 6 − 6 = 21 − 6
+ 6 and − 6 make zero.
Cross them out.
21 − 6 = 15.
21 − 6 = 15
Now we have 3x = 15.
3x = 15
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3x3 = 153
3 divided by 3 is 1.
So just x is left.
15 divided by 3 is 5.
153 = 5
So x = 5!
x = 5
Then x + 2 is 5 + 2 = 7.
The same answer.
It works!
x + 2 = 5 + 2 = 7
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Last: check.
Answer Careful: the question asks for x + 2, not x
▶ Watch it solved
The question
Question: if 6x + 9 = 33, what is 2x + 3?
6x + 9 = 33
We want 2x + 3.
Let's look for it inside the equation.
2x + 3 = ?
1 Compare the two
Look at 6x + 9 and 2x + 3.
We compare them part by part.
6 divided by 2 is 3.
So 6x is 3 times 2x.
6 ÷ 2 = 3, so 6x = 3 × 2x
9 divided by 3 is 3.
So 9 is 3 times 3.
9 ÷ 3 = 3, so 9 = 3 × 3
Every part of 6x + 9 is 3 times a part of 2x + 3.
2 Take out the 3
So we can write each part as 3 times.
3 × 2x + 3 × 3 = 33
3 times each part is the same as 3 times the whole bracket: 3(2x + 3).
Opening the bracket gives 6x + 9 back.
3(2x + 3) = 33
3 Remove the 3
3(2x + 3) means 3 times the bracket.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3(2x + 3)3 = 333
3 divided by 3 is 1.
So just the bracket is left.
33 divided by 3 is 11.
333 = 11
So 2x + 3 = 11!
2x + 3 = 11
Careful!
Many people find x and stop.
But the question asks for 2x + 3.
Careful: the question asks for 2x + 3, not x
4 Check
Let's check the long way: first we find x.
6x + 9 = 33
We want x by itself.
Two things are stuck to x: times 6 and + 9.
First x was times 6.
Then + 9.
To take them off, we go backwards.
First we remove the + 9.
Then the times 6.
x → × 6 → + 9
take off: − 9, then ÷ 6
To remove + 9, we take away 9.
We do it on both sides, so they stay equal.
6x + 9 − 9 = 33 − 9
+ 9 and − 9 make zero.
Cross them out.
33 − 9 = 24.
33 − 9 = 24
Now we have 6x = 24.
6x = 24
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
6x6 = 246
6 divided by 6 is 1.
So just x is left.
24 divided by 6 is 4.
246 = 4
So x = 4!
x = 4
Then 2x + 3 is 2 × 4 + 3 = 8 + 3 = 11.
The same answer.
It works!
2x + 3 = 2 × 4 + 3 = 8 + 3 = 11
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Last: check.
Answer Careful: the question asks for 2x + 3, not x
▶ Watch it solved
The question
Question: if 4x + 6 = 9, what is 2x + 3?
4x + 6 = 9
We want 2x + 3.
Let's look for it inside the equation.
2x + 3 = ?
1 Compare the two
Look at 4x + 6 and 2x + 3.
We compare them part by part.
4 divided by 2 is 2.
So 4x is 2 times 2x.
4 ÷ 2 = 2, so 4x = 2 × 2x
6 divided by 3 is 2.
So 6 is 2 times 3.
6 ÷ 3 = 2, so 6 = 2 × 3
Every part of 4x + 6 is 2 times a part of 2x + 3.
2 Take out the 2
So we can write each part as 2 times.
2 × 2x + 2 × 3 = 9
2 times each part is the same as 2 times the whole bracket: 2(2x + 3).
Opening the bracket gives 4x + 6 back.
2(2x + 3) = 9
3 Remove the 2
2(2x + 3) means 2 times the bracket.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2(2x + 3)2 = 92
2 divided by 2 is 1.
So just the bracket is left.
9/2 can't be made simpler.
So it stays a fraction.
So 2x + 3 = 9/2!
2x + 3 = 92
Careful!
Many people find x and stop.
But the question asks for 2x + 3.
Careful: the question asks for 2x + 3, not x
4 Check
Let's check the long way: first we find x.
4x + 6 = 9
We want x by itself.
Two things are stuck to x: times 4 and + 6.
First x was times 4.
Then + 6.
To take them off, we go backwards.
First we remove the + 6.
Then the times 4.
x → × 4 → + 6
take off: − 6, then ÷ 4
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
4x + 6 − 6 = 9 − 6
+ 6 and − 6 make zero.
Cross them out.
9 − 6 = 3.
9 − 6 = 3
Now we have 4x = 3.
4x = 3
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4x4 = 34
4 divided by 4 is 1.
So just x is left.
So x = 3/4!
x = 34
Then 2x + 3 is 2 × 3/4 + 3 = 3/2 + 3 = 9/2.
The same answer.
It works!
2x + 3 = 2 × 34 + 3 = 32 + 3 = 92
Let's look back.
First: compare the two.
Then: take out the 2.
Then: remove the 2.
Last: check.
Answer Careful: the question asks for 2x + 3, not x
▶ Watch it solved
