To determine the simplest form among the given expressions, we should inspect each option and see if it can be simplified further.
### Option A: [tex]\(7x - 3\)[/tex]
This expression is already in its simplest form. There are no denominators or additional terms that can be simplified further.
### Option B: [tex]\(\frac{7x - 27}{9}\)[/tex]
To check if this expression can be simplified, we'll look at the numerator [tex]\(7x - 27\)[/tex]. We need to see if it has any common factors with the denominator 9.
However, 7 and 27 do not have a common factor with 9. So, this expression cannot be simplified further.
### Option C: [tex]\(\frac{13x - 27}{9}\)[/tex]
Similarly, for this expression, we look at the numerator [tex]\(13x - 27\)[/tex]. We need to determine if it has any common factors with the denominator 9.
Again, 13 and 27 do not have a common factor with 9. Therefore, this expression cannot be simplified further.
### Option D: [tex]\(\frac{7x - 3}{9}\)[/tex]
To determine if this fraction can be simplified, we consider the numerator [tex]\(7x - 3\)[/tex]. Like in previous cases, we see if it shares any common factors with the denominator 9.
Here, 7 and 3 have no common factors with 9 either. So, this expression is already in its simplest form as well.
### Conclusion
Evaluating the simplest forms of all expressions, we see:
- Option A: [tex]\(7x - 3\)[/tex] is already simplified.
- Option B: [tex]\(\frac{7x - 27}{9}\)[/tex] cannot be simplified further but it's more complex due to the fraction and values.
- Option C: [tex]\(\frac{13x - 27}{9}\)[/tex] cannot be simplified further but it is also a complex fraction.
- Option D: [tex]\(\frac{7x - 3}{9}\)[/tex] is a fraction but again doesn't simplify further.
Considering simplicity in terms of fewer operations and clarity, Option A, [tex]\(7x - 3\)[/tex], is the most straightforward and simplest form.
Thus, the simplest form of the expression is:
Option A: [tex]\(7x - 3\)[/tex].
