To determine which expression does not represent "four more than one-third [tex]\( x \)[/tex]," let's break down what the phrase means mathematically.
The phrase "four more than one-third [tex]\( x \)[/tex]" can be written as:
[tex]\[ \frac{1}{3} x + 4 \][/tex]
Now, let's compare this expression with each of the given expressions:
1. [tex]\(\frac{1}{4} x + 3\)[/tex]
2. [tex]\(\frac{x}{3} + 4\)[/tex]
3. [tex]\(\frac{1}{3} x + 4\)[/tex]
We need to identify which of the above expressions does not match [tex]\(\frac{1}{3} x + 4\)[/tex].
### Comparing Each Expression:
1. Expression 1: [tex]\(\frac{1}{4} x + 3\)[/tex]:
- This expression has [tex]\(\frac{1}{4}\)[/tex] as the coefficient of [tex]\( x \)[/tex] and 3 as the constant term.
- Clearly, [tex]\(\frac{1}{4} x + 3 \neq \frac{1}{3} x + 4\)[/tex].
2. Expression 2: [tex]\(\frac{x}{3} + 4\)[/tex]:
- This expression has [tex]\(\frac{1}{3}\)[/tex] as the coefficient of [tex]\( x \)[/tex] and 4 as the constant term.
- We see that [tex]\(\frac{x}{3} + 4 = \frac{1}{3} x + 4\)[/tex].
3. Expression 3: [tex]\(\frac{1}{3} x + 4\)[/tex]:
- This expression exactly matches [tex]\(\frac{1}{3} x + 4\)[/tex].
From the above comparisons, it is clear that:
- The expression [tex]\(\frac{1}{4} x + 3\)[/tex] does not represent "four more than one-third [tex]\( x \)[/tex]".
Therefore, the expression that does not represent "four more than one-third [tex]\( x \)[/tex]" is:
[tex]\[ \boxed{\frac{1}{4} x + 3} \][/tex]
The position of this expression in the given list is:
[tex]\[ \boxed{0} \][/tex]
