Step by step
The question
Question: find x when f(x) = 2 for f(x) = x + 5.
f(x) = x + 5
f(x) = 2 means: the answer that comes out is 2.
We look for the x that goes in.
f(x) = 2: 2 comes out
find what goes in
Careful!
It is not f(2).
2 is what comes out, not what goes in.
Careful: not f(2) ✗
1 Write the equation
f(x) is x + 5.
So x + 5 = 2.
Now we solve it.
x + 5 = 2
2 Remove the + 5
We want x by itself.
The + 5 is in the way.
To remove + 5, we take away 5.
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.
x + 5 − 5 = 2 − 5
+ 5 and − 5 make zero.
Cross them out.
2 − 5 = −3.
2 − 5 = −3
So x = −3!
x = −3
3 Check
Let's check: put −3 into f.
We get 2.
f(−3) = (−3) + 5 = −3 + 5 = 2
So f(−3) = 2.
x = −3 is right!
Let's look back.
First: write the equation.
Then: remove the + 5.
Last: check.
Answer
x = −3