Step by step
The question
Question: find x and the length of the marked sides.
An isosceles triangle has sides 2x + 3 and 3x − 4.
1 Use the isosceles fact
Isosceles means two sides are equal.
The marks show which two.
So the two marked sides are equal: 2x + 3 = 3x − 4.
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 2x from the left 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.
3x − 2x = x.
Now we have 3 = x − 4.
Let's swap the two sides, so x is on the left.
3 Remove the − 4
We want x by itself.
The − 4 is in the way.
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
− 4 and + 4 make zero.
Cross them out.
3 + 4 = 7.
So x = 7!
4 Find the side
Put x = 7 in the side 2x + 3.
So each marked side is 17.
5 Check
Let's check: put x = 7 in the other side, 3x − 4.
We get 17 again: the sides are equal.
So x = 7 is right!
Let's look back.
First: use the isosceles fact.
Then: get x on one side.
Then: remove the − 4.
Then: find the side.
Last: check.