Question

Nine less than a numberis between 3 and 8. Find the range of numbers that make them true

Answer 1

To find the range of numbers for which 'nine less than a number is between 3 and 8', you need to solve the inequalities 3 < (n - 9) and (n - 9) < 8. The solution gives a range where n is greater than 12 and less than 17.

Step-by-step explanation:

The question asks for the range of numbers for which 'nine less than a number is between 3 and 8'. Let's denote the unknown number as 'n'. According to the given conditions, if we subtract 9 from 'n', it should result in a number between 3 and 8.

Mathematically, this can be written as:

• 3 < (n - 9)
• (n - 9) < 8

By solving these inequalities, we find:

1. Add 9 to the first inequality: n > 12
2. Add 9 to the second inequality: n < 17

Thus, the range for the number 'n' is:

12 < n < 17

Hence, any number greater than 12 and less than 17 would satisfy the condition that 'nine less than the number is between 3 and 8'.