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?
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)
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).