Let's solve the problem step-by-step.
1. Understanding the problem:
We need to find a number [tex]\( n \)[/tex] such that when 3 is subtracted from one third of this number, the result is less than 6.
2. Translating the problem into a mathematical inequality:
We start with the verbal statement:
"When 3 is subtracted from one third of a number [tex]\( n \)[/tex], the result is less than 6."
Mathematically, this can be written as:
[tex]$ \frac{1}{3} n - 3 < 6 $[/tex]
3. Isolating [tex]\( n \)[/tex]:
To solve for [tex]\( n \)[/tex], follow these steps:
a. Add 3 to both sides of the inequality:
[tex]$ \frac{1}{3} n - 3 + 3 < 6 + 3 $[/tex]
[tex]$ \frac{1}{3} n < 9 $[/tex]
b. Multiply both sides of the inequality by 3 to cancel the fraction:
[tex]$ 3 \cdot \frac{1}{3} n < 9 \cdot 3 $[/tex]
[tex]$ n < 27 $[/tex]
4. Conclusion:
The solution to the inequality is:
[tex]$ n < 27 $[/tex]
Therefore, the inequality and the correct solution representing this situation are:
[tex]$ \frac{1}{3} n - 3 < 6 ; n < 27 $[/tex]
So, the correct choice is:
[tex]$ \boxed{\frac{1}{3} n-3<6 ; n<27} $[/tex]
