# 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?

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Expert Answers

justaguide | Certified Educator

The statement we have is : the difference between a number and 3 is less than 15

Let the number be N.

The difference between N and 3 is |N - 3|

This is less than.

=> |N - 3| < 15

We have an inequality to solve. As we have the absolute value we get two inequalities.

N - 3 < 15

=> N < 18

3 - N < 15

=> N > -12

**Therefore the number can lie in the range ( -12, 18)**

hala718 | Certified Educator

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).**