6. \( 1-\frac{x}{3}-\frac{x+2}{6}=3 \)

Let's solve the equation step by step! First, we can simplify the equation. Start with: \( 1 - \frac{x}{3} - \frac{x+2}{6} = 3 \) To eliminate the fractions, we can multiply the whole equation by 6 (the least common multiple of the denominators 3 and 6): \( 6 \cdot 1 - 6 \cdot \frac{x}{3} - 6 \cdot \frac{x+2}{6} = 6 \cdot 3 \) This simplifies to: \( 6 - 2x - (x + 2) = 18 \) Distributing the negative sign gives us: \( 6 - 2x - x - 2 = 18 \) Combine like terms: \( 4 - 3x = 18 \) Next, isolate the variable term: \( -3x = 18 - 4 \) This simplifies to: \( -3x = 14 \) Now, divide both sides by -3: \( x = \frac{-14}{3} \) So, the solution to the equation \( 1 - \frac{x}{3} - \frac{x+2}{6} = 3 \) is: \( x = -\frac{14}{3} \) or approximately -4.67.