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