Step by step
The question
Question: find x when f(x) = −2 for f(x) = 3x + 4.
f(x) = −2 means: the answer that comes out is −2.
We look for the x that goes in.
Careful!
It is not f(−2).
−2 is what comes out, not what goes in.
1 Write the equation
f(x) is 3x + 4.
So 3x + 4 = −2.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 3 and + 4.
The + 4 is on the outside, so it comes off first.
Then the times 3.
2 Remove the + 4
To remove + 4, we take away 4.
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.
+ 4 and − 4 make zero.
Cross them out.
−2 − 4 = −6.
Now we have 3x = −6.
3 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
−6 divided by 3 is −2.
So x = −2!
4 Check
Let's check: put −2 into f.
We get −2.
So f(−2) = −2.
x = −2 is right!
Let's look back.
First: write the equation.
Then: remove the + 4.
Then: remove the 3.
Last: check.