Step by step
The question
Question: find x and the length of the marked sides.
An equilateral triangle has sides 2x + 1 and 4x − 9.
1 Use the equilateral fact
Equilateral means all three sides are equal.
The marks show it.
So the two marked sides are equal: 2x + 1 = 4x − 9.
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.
4x − 2x = 2x.
Now we have 1 = 2x − 9.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 2 and − 9.
The − 9 is on the outside, so it comes off first.
Then the times 2.
3 Remove the − 9
To remove − 9, we add 9.
We do it on both sides, so they stay equal.
− 9 and + 9 make zero.
Cross them out.
1 + 9 = 10.
Now we have 2x = 10.
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.
10 divided by 2 is 5.
So x = 5!
5 Find the side
Put x = 5 in the side 2x + 1.
So each marked side is 11.
6 Check
Let's check: put x = 5 in the other side, 4x − 9.
We get 11 again: the sides are equal.
So x = 5 is right!
Let's look back.
First: use the equilateral fact.
Then: get x on one side.
Then: remove the − 9.
Then: remove the 2.
Then: find the side.
Last: check.