I will now extract and solve the equations from the image you uploaded. Let me process and analyze the content.### Solutions to the equations:

1. Equation 1: $\frac{3}{x-1} = \frac{5}{2x+1}$

   Cross-multiply: $3(2x + 1) = 5(x - 1)$

   Expand: $6x + 3 = 5x - 5$

   Simplify: $x = -8$

   Answer: C) -8

2. Equation 2: $2x + 5 = 11$

   Subtract 5: $2x = 6$

   Divide by 2: $x = 3$

   Answer: B) x = 3

3. Equation 3: $\frac{3x + 1}{2} = 5$

   Multiply both sides by 2: $3x + 1 = 10$

   Subtract 1: $3x = 9$

   Divide by 3: $x = 3$

   Answer: A) x = 3

4. Equation 4: $\frac{x}{2} + 3 = 5$

   Subtract 3: $\frac{x}{2} = 2$

   Multiply by 2: $x = 4$

   Answer: B) x = 4

5. Equation 5: $3x - 2 = 16$

   Add 2: $3x = 18$

   Divide by 3: $x = 6$

   Answer: C) x = 6

6. Equation 6: $\frac{x}{4} - \frac{3}{20} = \frac{x}{5}$

   Find a common denominator (20): $\frac{5x}{20} - \frac{3}{20} = \frac{4x}{20}$

   Simplify: $\frac{5x - 3}{20} = \frac{4x}{20}$

   Cancel the denominator: $5x - 3 = 4x$

   Solve for $x$: $x = 3$

   Answer: A) x = 3

If you need further explanations or a breakdown of any specific question, let me know! Here are some related questions:

1. How do cross-multiplication rules work in fractions?
2. Why is it important to check for extraneous solutions in rational equations?
3. How can simplifying fractions help solve equations like in Question 6?
4. What is the significance of isolating $x$ in linear equations?
5. How do denominators affect the solving of fractional equations?

Tip: Always double-check solutions by plugging them back into the original equation!