Step by step
The question
Question: find x when f(x) = 9 for f(x) = 6 − x.
f(x) = 9 means: the answer that comes out is 9.
We look for the x that goes in.
Careful!
It is not f(9).
9 is what comes out, not what goes in.
1 Write the equation
f(x) is 6 − x.
So 6 − x = 9.
Now we solve it.
2 Remove the 6
We want x by itself.
The 6 is in the way.
To remove 6, we take away 6.
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.
6 and − 6 make zero.
Cross them out.
9 − 6 = 3.
Now we have −x = 3.
3 Remove the −1
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just x is left.
3 divided by −1 is −3.
So x = −3!
4 Check
Let's check: put −3 into f.
We get 9.
So f(−3) = 9.
x = −3 is right!
Let's look back.
First: write the equation.
Then: remove the 6.
Then: remove the −1.
Last: check.