The equation is $$\frac{3x+5}{5} - \frac{x+1}{3} = 1$$.

This is a math problem that involves solving a linear equation with fractions. Here's how we can solve it step-by-step:

1. Find a common denominator: The denominators are 5 and 3. The least common multiple of 5 and 3 is 15.
2. Multiply each term by the common denominator:
• Multiply $$\frac{3x+5}{5}$$ by 15: \( \frac{15(3x+5)}{5} = 3(3x+5) = 9x + 15 \)
• Multiply $$\frac{x+1}{3}$$ by 15: \( \frac{15(x+1)}{3} = 5(x+1) = 5x + 5 \)
• Multiply 1 by 15: \( 15 \times 1 = 15 \)
3. Rewrite the equation with the new terms: \( (9x + 15) - (5x + 5) = 15 \)
4. Simplify the equation:
• Distribute the negative sign: \( 9x + 15 - 5x - 5 = 15 \)
• Combine like terms: \( (9x - 5x) + (15 - 5) = 15 \)
• \( 4x + 10 = 15 \)
5. Isolate the variable (x):
• Subtract 10 from both sides: \( 4x = 15 - 10 \)
• \( 4x = 5 \)
6. Solve for x:
• Divide both sides by 4: \( x = \frac{5}{4} \)

Answer:

x = 5/4