Step by step
The question
Question: if 5x − 10 = 30, what is x − 2?
We want x − 2.
Let's look for it inside the equation.
1 Compare the two
Look at 5x − 10 and x − 2.
We compare them part by part.
5x is 5 times x.
10 divided by 2 is 5.
So 10 is 5 times 2.
Every part of 5x − 10 is 5 times a part of x − 2.
2 Take out the 5
So we can write each part as 5 times.
5 times each part is the same as 5 times the whole bracket: 5(x − 2).
Opening the bracket gives 5x − 10 back.
3 Remove the 5
5(x − 2) means 5 times the bracket.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just the bracket is left.
30 divided by 5 is 6.
So x − 2 = 6!
Careful!
Many people find x and stop.
But the question asks for x − 2.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 5 and − 10.
First x was times 5.
Then − 10.
To take them off, we go backwards.
First we remove the − 10.
Then the times 5.
To remove − 10, we add 10.
We do it on both sides, so they stay equal.
− 10 and + 10 make zero.
Cross them out.
30 + 10 = 40.
Now we have 5x = 40.
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
40 divided by 5 is 8.
So x = 8!
Then x − 2 is 8 − 2 = 6.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 5.
Then: remove the 5.
Last: check.