Step by step
The question
Question: solve (2x − 1)/5 = (x + 3)/4.
Two fractions are equal.
1 Cross multiply
When two fractions are equal, we can cross multiply.
These two are equal.
Work out the multiplications.
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.
Work out each multiplication.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 5x from the right side.
To remove 5x, we take away 5x.
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.
5x and − 5x make zero.
Cross them out.
8x − 5x = 3x.
Now we have 3x − 4 = 15.
We want x by itself.
Two things are stuck to x: times 3 and − 4.
The − 4 is on the outside, so it comes off first.
Then the times 3.
4 Remove the − 4
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
− 4 and + 4 make zero.
Cross them out.
15 + 4 = 19.
Now we have 3x = 19.
5 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
So x = 19/3!
6 Check
Let's check: put 19/3 in place of x.
First the left side.
Now the right side.
Both sides are 140/3.
So x = 19/3 is right!
Let's look back.
First: cross multiply.
Then: open the brackets.
Then: get x on one side.
Then: remove the − 4.
Then: remove the 3.
Last: check.