Step by step
The question
Question: solve 10/x − 3 = 2.
x is at the bottom of a fraction.
First: a bottom can never be 0.
We can't divide by 0.
x at the bottom can't be 0.
So x ≠ 0.
1 Remove the fractions
The bottom is x.
Times x will remove it.
We multiply every part by x.
We do it on both sides, so they stay equal.
Each bottom goes into x.
So in each fraction, we can cross out the bottom.
What is left of x stays.
x divided by x is 1.
x times 3 is 3x.
x times 2 is 2x.
This is what is left of x in each part.
We write the equation again.
No more fractions!
2 Get x on one side
There is x on both sides.
We want x on one side only.
The numbers in front of x are −3 and 2.
We remove the smaller one, −3x, so the x part that is left is plus.
So we remove the −3x from the left side.
To remove −3x, we add 3x.
We do it on both sides, so they stay equal.
− 3x and + 3x cancel each other.
They make zero.
2x + 3x = 5x.
Now we have 10 = 5x.
Let's swap the two sides, so x is on the left.
Both sides are the same amount, so we can swap them.
So after step 2: we added 3x, and now we have 5x = 10.
Is x alone now?
Not yet: 5x means 5 times x.
How do we remove it?
3 Remove the 5
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
They cancel each other.
So just x is left.
10 divided by 5 is 2.
So x = 2!
4 Check
Let's check: put 2 in place of x.
First the left side.
Now the right side.
Both sides are 2.
So x = 2 is right!
Let's look back.
First: remove the fractions.
Then: get x on one side.
Then: remove the 5.
Last: check.