Step by step
The question
Question: solve 8/x − 3 = 1.
First: a bottom can never be 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.
x divided by x is 1.
x times 3 is 3x.
x times 1 is x.
Write what is left.
No more fractions!
2 Get x on one side
There is x on both sides.
We want x on one side only.
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 make zero.
Cross them out.
x + 3x = 4x.
Now we have 8 = 4x.
Let's swap the two sides, so x is on the left.
3 Remove the 4
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.
4 divided by 4 is 1.
So just x is left.
8 divided by 4 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 1.
So x = 2 is right!
Let's look back.
First: remove the fractions.
Then: get x on one side.
Then: remove the 4.
Last: check.