Step by step
The question
Question: find x when f(x) = 6 for f(x) = 2x + 6.
f(x) = 6 means: the answer that comes out is 6.
We look for the x that goes in.
Careful!
It is not f(6).
6 is what comes out, not what goes in.
1 Write the equation
f(x) is 2x + 6.
So 2x + 6 = 6.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 2 and + 6.
The + 6 is on the outside, so it comes off first.
Then the times 2.
2 Remove the + 6
To remove + 6, we take away 6.
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.
+ 6 and − 6 make zero.
Cross them out.
6 − 6 = 0.
Now we have 2x = 0.
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.
0 divided by 2 is 0.
So x = 0!
4 Check
Let's check: put 0 into f.
We get 6.
So f(0) = 6.
x = 0 is right!
Let's look back.
First: write the equation.
Then: remove the + 6.
Then: remove the 2.
Last: check.