Step by step
The question
Question: find x.
C and D are on the same side of AB.
The angles at C and D are 3x − 10 and x + 30.
1 Use the circle rule
The line AB cuts the circle into two parts, called segments.
C and D are in the same part.
Both angles stand on the same arc: the orange part, from A to B.
Look at the angle at the center on that arc.
The circle rule says it is double each of them.
Both angles are half of the same angle.
So they are equal.
So the two angles are equal: 3x − 10 = x + 30.
2 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the x from the right side.
To remove x, we take away x.
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.
x and − x make zero.
Cross them out.
3x − x = 2x.
Now we have 2x − 10 = 30.
We want x by itself.
Two things are stuck to x: times 2 and − 10.
The − 10 is on the outside, so it comes off first.
Then the times 2.
3 Remove the − 10
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 2x = 40.
4 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
40 divided by 2 is 20.
So x = 20!
5 Check
Let's check: put x = 20 in each angle.
Both angles are 50°.
They are equal, so x = 20 is right!
Let's look back.
First: use the circle rule.
Then: get x on one side.
Then: remove the − 10.
Then: remove the 2.
Last: check.