How do we write and solve the statement the difference betw

How do we write and solve the statement \" the difference between a number and 3 is less than 15\" What are possible values of the number?

Solution

Let us assume that the number required is x.

Then we need to find the difference.

==> l x - 3l < 15

Now we will solve the inequality with the absolute value.

We will rewrite:

==> -15 < x-3 < 15

Now we will add 3 to both sides.

==> -12 < x < 18

Then the values of the number are the interval (-12, 18).