Simplify the expression $x - \frac{x+1}{6}$.

1. Problem Description

Simplify the expression $x - \frac{x+1}{6}$.

2. Solution Steps

To simplify the expression, we need to combine the two terms. First, we can rewrite $x$ as a fraction with a denominator of 6:

$x = \frac{6x}{6}$.

Now we can rewrite the expression as:

$\frac{6x}{6} - \frac{x+1}{6}$.

Since the fractions have the same denominator, we can combine the numerators:

$\frac{6x - (x+1)}{6}$.

Distribute the negative sign in the numerator:

$\frac{6x - x - 1}{6}$.

Combine like terms in the numerator:

$\frac{5x - 1}{6}$.

3. Final Answer

$\frac{5x-1}{6}$