Step by step
The question
Question: find x when f(x) = −1 for f(x) = 3x − 7.
f(x) = −1 means: the answer that comes out is −1.
We look for the x that goes in.
Careful!
It is not f(−1).
−1 is what comes out, not what goes in.
1 Write the equation
f(x) is 3x − 7.
So 3x − 7 = −1.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 3 and − 7.
The − 7 is on the outside, so it comes off first.
Then the times 3.
2 Remove the − 7
To remove − 7, we add 7.
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.
− 7 and + 7 make zero.
Cross them out.
−1 + 7 = 6.
Now we have 3x = 6.
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.
6 divided by 3 is 2.
So x = 2!
4 Check
Let's check: put 2 into f.
We get −1.
So f(2) = −1.
x = 2 is right!
Let's look back.
First: write the equation.
Then: remove the − 7.
Then: remove the 3.
Last: check.