Step by step
The question
Question: find x when the angles on a straight line are 5x − 10 and 3x + 30.
1 Use the angle fact
Angles on a straight line add up to 180°.
A straight line is half a turn.
So we add them all and make it 180: 5x − 10 + 3x + 30 = 180.
2 Group like terms
The x terms go together.
The plain numbers go together.
Now we have 8x + 20 = 180.
3 Remove the + 20
We want 8x by itself.
The + 20 is in the way.
To remove + 20, we take away 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.
180 minus 20 is 160.
4 Remove the 8
8x means 8 times x.
We want just x.
To remove times 8, we divide by 8.
We do it on both sides, so they stay equal.
8 divided by 8 is 1.
So just x is left.
160 divided by 8 is 20.
So x = 20.
5 Check
Let's check: put x = 20 in each angle.
Now add all the angles.
They add up to 180°.
So x = 20 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 20.
Then: remove the 8.
Last: check.