Step by step
The question
Question: if x − 4 = 5, what is 3x − 12?
We want 3x − 12.
Let's look for it inside the equation.
1 Compare the two
Look at 3x − 12 and x − 4.
We compare them part by part.
3x is 3 times x.
12 divided by 4 is 3.
So 12 is 3 times 4.
Every part of 3x − 12 is 3 times a part of x − 4.
2 Multiply by 3
So we multiply both sides by 3.
We do it on both sides, so they stay equal.
Times 3 goes to every part.
3 times 5 is 15.
Careful!
Both sides are times 3.
5 becomes 15.
3 times x is 3x.
3 times −4 is −12.
So 3x − 12 = 15!
3 Check
Let's check the long way: first we find x.
We want x by itself.
The − 4 is in the way.
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
− 4 and + 4 make zero.
Cross them out.
5 + 4 = 9.
So x = 9!
Then 3x − 12 is 3 × 9 − 12 = 27 − 12 = 15.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: multiply by 3.
Last: check.