- Example of inequality problem solving 2
- Question:
- The average (arthmetic mean) of five numbers is greater than nine and less than eleven. What is one possible number that could be the sum of these five numbers?

- Solution:
- the 5 number is: x
_{1}, x_{2}, x_{3}, x_{4}, x_{5} - the average of 5 number is: (x
_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5})/5 - Given: the average of five numbers is greater than 9 and less than 11
- so we get the inequality:
- 9 < (x
_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5})/5 < 11 - multiply 5 in each term in the inequality
- 45 < (x
_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}) < 55 - the possible values of (x
_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}) are: 46, 47, 48, 49, 50, 51, 52, 53, 54 - so 46 is one possible value

What is the average of five numbers? The average of five numbers is that the sum of the five numbers divide by five. Given that the average of five numbers is greater than nine and less than eleven, so we get the compound inequality. A compound inequality can divide into two inequalities. Multiply the denominator in each of the inequalities to get the sum of the five numbers. Thus we get the range of the five numbers.