Step by step
The question
Question: find x when f(x) = 11 for f(x) = −2x + 5.
f(x) = 11 means: the answer that comes out is 11.
We look for the x that goes in.
Careful!
It is not f(11).
11 is what comes out, not what goes in.
1 Write the equation
f(x) is −2x + 5.
So −2x + 5 = 11.
Now we solve it.
We want x by itself.
Two things are stuck to x: times −2 and + 5.
The + 5 is on the outside, so it comes off first.
Then the times −2.
2 Remove the + 5
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.
+ 5 and − 5 make zero.
Cross them out.
11 − 5 = 6.
Now we have −2x = 6.
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.
6 divided by −2 is −3.
So x = −3!
4 Check
Let's check: put −3 into f.
We get 11.
So f(−3) = 11.
x = −3 is right!
Let's look back.
First: write the equation.
Then: remove the + 5.
Then: remove the −2.
Last: check.