Step by step
The question
Question: find x and the length of the marked sides.
An isosceles triangle has sides 5x − 2 and 3x + 6.
1 Use the isosceles fact
Isosceles means two sides are equal.
The marks show which two.
So the two marked sides are equal: 5x − 2 = 3x + 6.
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 3x from the right side.
To remove 3x, we take away 3x.
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.
3x and − 3x make zero.
Cross them out.
5x − 3x = 2x.
Now we have 2x − 2 = 6.
We want x by itself.
Two things are stuck to x: times 2 and − 2.
The − 2 is on the outside, so it comes off first.
Then the times 2.
3 Remove the − 2
To remove − 2, we add 2.
We do it on both sides, so they stay equal.
− 2 and + 2 make zero.
Cross them out.
6 + 2 = 8.
Now we have 2x = 8.
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.
8 divided by 2 is 4.
So x = 4!
5 Find the side
Put x = 4 in the side 5x − 2.
So each marked side is 18.
6 Check
Let's check: put x = 4 in the other side, 3x + 6.
We get 18 again: the sides are equal.
So x = 4 is right!
Let's look back.
First: use the isosceles fact.
Then: get x on one side.
Then: remove the − 2.
Then: remove the 2.
Then: find the side.
Last: check.