Step by step
The question
Question: solve 5 = 20/(x − 1).
x is in the bottom of a fraction.
We write 5 as 5/1.
Now both sides are fractions.
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
Work out the multiplications.
2 Remove the 5
The 5 multiplies the whole bracket.
Easy way: remove the 5 first.
To remove times 5, we divide by 5.
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.
5 divided by 5 is 1.
So just the bracket is left.
20 divided by 5 is 4.
Now we have x − 1 = 4.
We don't need the bracket any more.
3 Remove the − 1
We want x by itself.
The − 1 is in the way.
To remove − 1, we add 1.
We do it on both sides, so they stay equal.
− 1 and + 1 make zero.
Cross them out.
4 + 1 = 5.
So x = 5!
4 Check
Let's check: put 5 in place of x.
First the left side.
Now the right side.
Both sides are 5.
So x = 5 is right!
Let's look back.
First: cross multiply.
Then: remove the 5.
Then: remove the − 1.
Last: check.