Step by step
The question
Question: find x when f(x) = 7 for f(x) = 2x − 3.
f(x) = 7 means: the answer that comes out is 7.
We look for the x that goes in.
Careful!
It is not f(7).
7 is what comes out, not what goes in.
1 Write the equation
f(x) is 2x − 3.
So 2x − 3 = 7.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 2 and − 3.
The − 3 is on the outside, so it comes off first.
Then the times 2.
2 Remove the − 3
To remove − 3, we add 3.
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.
− 3 and + 3 make zero.
Cross them out.
7 + 3 = 10.
Now we have 2x = 10.
3 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!
4 Check
Let's check: put 5 into f.
We get 7.
So f(5) = 7.
x = 5 is right!
Let's look back.
First: write the equation.
Then: remove the − 3.
Then: remove the 2.
Last: check.