Step by step
The question
Question: find x and the length of the marked sides.
An isosceles triangle has sides x + 9 and 4x.
1 Use the isosceles fact
Isosceles means two sides are equal.
The marks show which two.
So the two marked sides are equal: x + 9 = 4x.
Careful!
The marks say the sides are the same length.
So we write one equals the other.
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 left 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.
4x − x = 3x.
Now we have 9 = 3x.
Let's swap the two sides, so x is on the left.
3 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
9 divided by 3 is 3.
So x = 3!
4 Find the side
Put x = 3 in the side x + 9.
So each marked side is 12.
5 Check
Let's check: put x = 3 in the other side, 4x.
We get 12 again: the sides are equal.
So x = 3 is right!
Let's look back.
First: use the isosceles fact.
Then: get x on one side.
Then: remove the 3.
Then: find the side.
Last: check.