Step by step
The question
Question: find x when f(x) = 13 for f(x) = 3x + 1.
f(x) = 13 means: the answer that comes out is 13.
We look for the x that goes in.
Careful!
It is not f(13).
13 is what comes out, not what goes in.
1 Write the equation
f(x) is 3x + 1.
So 3x + 1 = 13.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 3 and + 1.
The + 1 is on the outside, so it comes off first.
Then the times 3.
2 Remove the + 1
To remove + 1, we take away 1.
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.
+ 1 and − 1 make zero.
Cross them out.
13 − 1 = 12.
Now we have 3x = 12.
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.
12 divided by 3 is 4.
So x = 4!
4 Check
Let's check: put 4 into f.
We get 13.
So f(4) = 13.
x = 4 is right!
Let's look back.
First: write the equation.
Then: remove the + 1.
Then: remove the 3.
Last: check.