Step by step
The question
Question: find x when f(x) = 8 for f(x) = 5x − 2.
f(x) = 8 means: the answer that comes out is 8.
We look for the x that goes in.
Careful!
It is not f(8).
8 is what comes out, not what goes in.
1 Write the equation
f(x) is 5x − 2.
So 5x − 2 = 8.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 5 and − 2.
The − 2 is on the outside, so it comes off first.
Then the times 5.
2 Remove the − 2
To remove − 2, we add 2.
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.
− 2 and + 2 make zero.
Cross them out.
8 + 2 = 10.
Now we have 5x = 10.
3 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
10 divided by 5 is 2.
So x = 2!
4 Check
Let's check: put 2 into f.
We get 8.
So f(2) = 8.
x = 2 is right!
Let's look back.
First: write the equation.
Then: remove the − 2.
Then: remove the 5.
Last: check.