Step by step
The question
Question: if 10x − 15 = 25, what is 2x − 3?
We want 2x − 3.
Let's look for it inside the equation.
1 Compare the two
Look at 10x − 15 and 2x − 3.
We compare them part by part.
10 divided by 2 is 5.
So 10x is 5 times 2x.
15 divided by 3 is 5.
So 15 is 5 times 3.
Every part of 10x − 15 is 5 times a part of 2x − 3.
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(2x − 3).
Opening the bracket gives 10x − 15 back.
3 Remove the 5
5(2x − 3) 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.
25 divided by 5 is 5.
So 2x − 3 = 5!
Careful!
Many people find x and stop.
But the question asks for 2x − 3.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 10 and − 15.
First x was times 10.
Then − 15.
To take them off, we go backwards.
First we remove the − 15.
Then the times 10.
To remove − 15, we add 15.
We do it on both sides, so they stay equal.
− 15 and + 15 make zero.
Cross them out.
25 + 15 = 40.
Now we have 10x = 40.
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
We do it on both sides, so they stay equal.
10 divided by 10 is 1.
So just x is left.
40 divided by 10 is 4.
So x = 4!
Then 2x − 3 is 2 × 4 − 3 = 8 − 3 = 5.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 5.
Then: remove the 5.
Last: check.