Question

Gerald is thinking of a number n, and he wants his sister to guess the number. His first clue is that 7 more than 3 times his

number is at least 10 and at most 28. Write a compound inequality that shows the range of numbers that Isabella might be
thinking of.
Write your answer in interval notation. For example-3

Answer 1

(1, 7)

Explanation:

The number is n.

7 more than 3 times his

number is at least 10 and at most 28.

Thus;

10 ≤ 3n + 7 ≤ 28

Let's solve individually;

10 ≤ 3n + 7

10 - 7 ≤ 3n

n ≥ 3/3

n ≥ 1

Also,

3n + 7 ≤ 28

3n ≤ 28 - 7

3n ≤ 21

n ≤ 21/3

n ≤ 7

Thus, since n cannot be more than 7 or less than 1, it means in interval Notation, the answer is;

(1, 7)