In relation to a larger number x, how is the smaller number defined, which is 6 less than one-third of x?

The smaller number is defined as being 6 less than one-third of a larger number ( x ). To denote one-third of ( x ), you would mathematically express it as ( \frac{x}{3} ).

To find the smaller number, you take this value and subtract 6 from it. Hence, the expression can be written as:

[

\frac{x}{3} - 6

]

This matches the definition given in the question. The choice that reflects this correct expression is ( x/3 - 6 ).

The other options do not accurately describe the condition presented in the question. For example, ( 3/x + 6 ) introduces a division that does not relate to one-third of ( x ), while ( 3x - 6 ) incorrectly multiplies ( x ) rather than dividing it by 3. Finally, ( 6 - 3/x ) changes the operation entirely and does not resemble the defined relationship between the larger number ( x ) and the smaller number. Thus, the expression ( \frac{x}{3} - 6 ) remains the only correct formulation of the situation provided in the question.