Step by step
The question
Question: find x.
One angle of an equilateral triangle is 4x − 20.
1 Use the equilateral fact
Equilateral means all three sides are equal.
The marks show it.
Equal sides make equal angles.
So all three angles are the same.
They add up to 180°.
180 shared by 3 is 60.
So every angle is 60°.
So 4x − 20 = 60.
Careful!
One angle is not the whole 180°.
It is one third of it: 60°.
We want x by itself.
Two things are stuck to x: times 4 and − 20.
The − 20 is on the outside, so it comes off first.
Then the times 4.
2 Remove the − 20
To remove − 20, we add 20.
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.
− 20 and + 20 make zero.
Cross them out.
60 + 20 = 80.
Now we have 4x = 80.
3 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
80 divided by 4 is 20.
So x = 20!
4 Check
Let's check: put x = 20 in the angle.
We get 60°.
So x = 20 is right!
Let's look back.
First: use the equilateral fact.
Then: remove the − 20.
Then: remove the 4.
Last: check.