f(x) = 7 - 2x, find x when f(x) = -3 Step by Step

Step by step

The question

Question: find x when f(x) = −3 for f(x) = 7 − 2x.

f(x) = 7 − 2x

f(x) = −3 means: the answer that comes out is −3.

We look for the x that goes in.

f(x) = −3: −3 comes out

find what goes in

Careful!

It is not f(−3).

−3 is what comes out, not what goes in.

Careful: not f(−3) ✗

1 Write the equation

f(x) is 7 − 2x.

So 7 − 2x = −3.

Now we solve it.

7 − 2x = −3

We want x by itself.

Two things are stuck to x: times −2 and + 7.

The + 7 is on the outside, so it comes off first.

Then the times −2.

2 Remove the 7

To remove 7, we take away 7.

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.

7 − 2x ~~− 7~~ = −3 − 7

7 and − 7 make zero.

Cross them out.

−3 − 7 = −10.

−3 − 7 = −10

Now we have −2x = −10.

−2x = −10

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.

−2x−2 = −10−2

−2 divided by −2 is 1.

So just x is left.

−10 divided by −2 is 5.

−10−2 = 5

So x = 5!

x = 5

4 Check

Let's check: put 5 into f.

We get −3.

f(5) = 7 − 2(5) = 7 − 10 = −3

So f(5) = −3.

x = 5 is right!

Let's look back.

First: write the equation.

Then: remove the 7.

Then: remove the −2.

Last: check.

Answer