Step by step
The question
Question: find x.
The base angles of an isosceles triangle are 4x − 10 and 2x + 30.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two.
Fold it on the dashed line, from the top to the middle of the base.
The two halves fit exactly.
So the two angles at the base fit on each other.
The base angles are equal.
So the two base angles are equal: 4x − 10 = 2x + 30.
Now we solve it.
Careful!
The equal angles are the two at the base, between the base and an equal side.
2 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the right side.
To remove 2x, we take away 2x.
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.
2x and − 2x make zero.
Cross them out.
4x − 2x = 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 base angle.
Both base angles are 70°.
They are equal, so x = 20 is right!
Let's look back.
First: use the isosceles fact.
Then: get x on one side.
Then: remove the − 10.
Then: remove the 2.
Last: check.