f(x) = 5 - 3x, find x when f(x) = 5

Step by step

The question

Question: find x when f(x) = 5 for f(x) = 5 − 3x.

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 5 − 3x.

So 5 − 3x = 5.

Now we solve it.

We want x by itself.

Two things are stuck to x: times −3 and + 5.

The + 5 is on the outside, so it comes off first.

Then the times −3.

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.

5 − 5 = 0.

Now we have −3x = 0.

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.

0 divided by −3 is 0.

So x = 0!

4 Check

Let's check: put 0 into f.

We get 5.

So f(0) = 5.

x = 0 is right!

Let's look back.

First: write the equation.

Then: remove the 5.

Then: remove the −3.

Last: check.