Question

Nidhi is thinking of a number n, and she wants her sister to guess the number. Her first clue is that eight less than three times her number is between one and nineteen. Write a compound inequality that shows the range of numbers that Nidhi might be thinking of

Answer 1

The range of numbers that Nidhi might be thinking of is between 3 and 9.

Explanation:

We are given that Nidhi is thinking of a number n, and she wants her sister to guess the number.

Her first clue is that eight less than three times her number is between one and nineteen.

Let the number Nidhi is thinking be 'n'.

So, eight less than three times her number means that;

`(3* \text{n}) - 8 = 3\text{n}-8`

Now, according to the question; the above equation is between one and nineteen, so;

`1< 3\text{n}-8 < 19`

Adding 8 to the whole expression;

`1+8< 3\text{n}-8 +8< 19+8`

`9< 3\text{n}< 27`

Dividing the whole expression by 3;

`(9)/(3) < \frac{3\text{n}}{3} < (27)/(3)`

`3< \text{n}< 9`

Hence, the range of numbers that Nidhi might be thinking of is between 3 and 9.