Step by step
The question
Question: solve (x + 1)/3 = (x − 1)/2.
Two fractions are equal.
1 Cross multiply
When two fractions are equal, we can cross multiply.
Why?
We multiply both sides by both bottoms: 3 and 2.
On the left, 3/3 is 1.
So (x + 1) times 2 is left.
On the right, 2/2 is 1.
So (x − 1) times 3 is left.
That is the cross.
These two are equal.
We write them the short way, without the × sign.
2 Open the brackets
What is in front of a bracket multiplies every part inside.
So we write each part times what is in front.
Watch the signs.
2 times x is 2x.
2 times 1 is 2.
3 times x is 3x.
3 times (−1) is −3.
3 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 2 and 3.
We remove the smaller one, 2x.
Then the x part that is left is plus.
A plus x part is easier to work with.
So we remove the 2x from the left side.
To remove 2x, we take away 2x.
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.
2x and − 2x make zero.
Cross them out.
3x − 2x = x.
Now we have 2 = x − 3.
Let's swap the two sides, so x is on the left.
Both sides are the same amount, so we can swap them.
4 Remove the − 3
We want x by itself.
The − 3 is in the way.
To remove − 3, we add 3.
We do it on both sides, so they stay equal.
− 3 and + 3 make zero.
Cross them out.
2 + 3 = 5.
So x = 5!
5 Check
Let's check: put 5 in place of x.
First the left side.
Now the right side.
Both sides are 2.
So x = 5 is right!
6 Type it in
The answer box takes 5 characters.
5 has 1.
It fits.
We type 5.
Let's look back.
First: cross multiply.
Then: open the brackets.
Then: get x on one side.
Then: remove the − 3.
Then: check.
Last: type it in.