The question
Question: solve x/6 = 2/3.
Two fractions are equal.
x6 = 23
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
x × 3 = 2 × 6
Work out the multiplications.
3x = 12
2 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
3x3 = 123
3 divided by 3 is 1.
So just x is left.
12 divided by 3 is 4.
123 = 4
So x = 4!
x = 4
3 Check
Let's check: put 4 in place of x.
First the left side.
Left: 46 = 4÷26÷2 = 23
Now the right side.
Right: 23
Both sides are 2/3.
So x = 4 is right!
Both sides equal 23
Let's look back.
First: cross multiply.
Then: remove the 3.
Last: check.
▶ Watch it solved
The question
Question: solve 12/x = 3.
x is in the bottom of a fraction.
12x = 3
We write 3 as 3/1.
Now both sides are fractions.
12x = 31
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
12 × 1 = 3 × x
Work out the multiplications.
12 = 3x
Let's swap the two sides, so x is on the left.
3x = 12
2 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
3x3 = 123
3 divided by 3 is 1.
So just x is left.
12 divided by 3 is 4.
123 = 4
So x = 4!
x = 4
3 Check
Let's check: put 4 in place of x.
First the left side.
Left: 124 = 3
Now the right side.
Right: 3
Both sides are 3.
So x = 4 is right!
Both sides equal 3
Let's look back.
First: cross multiply.
Then: remove the 3.
Last: check.
▶ Watch it solved
The question
Question: solve (x + 1)/(x − 2) = 4.
x is in the bottom of a fraction.
x + 1x − 2 = 4
We write 4 as 4/1.
Now both sides are fractions.
x + 1x − 2 = 41
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
(x + 1) × 1 = 4 × (x − 2)
Work out the multiplications.
(x + 1) = 4(x − 2)
2 Open the brackets
The 4 in front of the bracket multiplies every part inside.
So we write 4 times each part.
A bracket with a plus or nothing in front can just be removed.
x + 1 = 4 × x + 4 × (−2)
Work out each multiplication.
x + 1 = 4x − 8
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the x from the left side.
To remove x, we take away x.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
x + 1 − x = 4x − 8 − x
x and − x make zero.
Cross them out.
4x − x = 3x.
4x − x = 3x
Now we have 1 = 3x − 8.
1 = 3x − 8
Let's swap the two sides, so x is on the left.
3x − 8 = 1
We want x by itself.
Two things are stuck to x: times 3 and − 8.
The − 8 is on the outside, so it comes off first.
Then the times 3.
4 Remove the − 8
To remove − 8, we add 8.
We do it on both sides, so they stay equal.
3x − 8 + 8 = 1 + 8
− 8 and + 8 make zero.
Cross them out.
1 + 8 = 9.
1 + 8 = 9
Now we have 3x = 9.
3x = 9
5 Remove the 3
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 = 93
3 divided by 3 is 1.
So just x is left.
9 divided by 3 is 3.
93 = 3
So x = 3!
x = 3
6 Check
Let's check: put 3 in place of x.
First the left side.
Left: 3 + 13 − 2 = 41 = 4
Now the right side.
Right: 4
Both sides are 4.
So x = 3 is right!
Both sides equal 4
Let's look back.
First: cross multiply.
Then: open the brackets.
Then: get x on one side.
Then: remove the − 8.
Then: remove the 3.
Last: check.
▶ Watch it solved
