Step by step
The question
Question: solve (x − 1)/3 = 5/6.
Two fractions are equal.
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
Work out the multiplications.
2 Open the brackets
The 6 in front of the bracket multiplies every part inside.
So we write 6 times each part.
Work out each multiplication.
We want x by itself.
Two things are stuck to x: times 6 and − 6.
The − 6 is on the outside, so it comes off first.
Then the times 6.
3 Remove the − 6
To remove − 6, we add 6.
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.
− 6 and + 6 make zero.
Cross them out.
15 + 6 = 21.
Now we have 6x = 21.
4 Remove the 6
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.
6 divided by 6 is 1.
So just x is left.
We can make 21/6 simpler.
It is the same as 7/2.
So x = 7/2!
5 Check
Let's check: put 7/2 in place of x.
We get 15, the same as the right side.
So x = 7/2 is right!
Let's look back.
First: cross multiply.
Then: open the brackets.
Then: remove the − 6.
Then: remove the 6.
Last: check.