Step by step
The question
Question: solve 6/x + 1 = 4.
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.
There are four choices.
First we solve it, the normal way.
Then we pick.
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 1 is x.
x times 4 is 4x.
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 1 and 4.
We remove the smaller one, x, so the x part that is left is plus.
So we remove the x from the left side.
To remove x, we take away x.
We do it on both sides, so they stay equal.
+ x and − x cancel each other.
They make zero.
4x − x = 3x.
Now we have 6 = 3x.
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 took away x, and now we have 3x = 6.
Is x alone now?
Not yet: 3x means 3 times x.
How do we remove it?
3 Remove the 3
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
They cancel each other.
So just x is left.
6 divided by 3 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 4.
So x = 2 is right!
5 Pick the choice
Our answer is x = 2.
That is choice C.
6 Why not the others
A is 1/2.
Wrong: 3/6: upside down, x = 6 ÷ 3.
B is 6/5.
Wrong: added 1: 6/x = 5.
D is 18.
Wrong: 6 × 3: multiplied instead of dividing.
Let's look back.
First: remove the fractions.
Then: get x on one side.
Then: remove the 3.
Then: check.
Then: pick the choice.
Last: why not the others.