I will transcribe and solve the equations from the image for you. Let's tackle each question one by one.

1. The solution to $3(x - 5) + 4x = 8x + 4$

• Simplify: $3(x - 5) = 3x - 15$, $3x - 15 + 4x = 8x + 4$, Combine like terms: $7x - 15 = 8x + 4$, Subtract $7x$ from both sides: $-15 = x + 4$, Subtract $4$ from both sides: $x = -19$.

Answer: $x = -19$.

2. The solution to $-\frac{3}{2}(1 - 4x) = 3x + 8$

• Expand: $-\frac{3}{2}(1 - 4x) = -\frac{3}{2} + 6x$, Equation becomes: $-\frac{3}{2} + 6x = 3x + 8$, Subtract $3x$ from both sides: $-\frac{3}{2} + 3x = 8$, Add $\frac{3}{2}$ to both sides: $3x = 8 + \frac{3}{2} = \frac{16}{2} + \frac{3}{2} = \frac{19}{2}$, Solve for $x$: $x = \frac{19}{6}$.

Answer: $x = \frac{19}{6}$.

3. The solution to $2 + 3(2a + 1) = 3(a + 2)$

• Expand: $3(2a + 1) = 6a + 3$, $3(a + 2) = 3a + 6$, Combine terms: $2 + 6a + 3 = 3a + 6$, Simplify: $6a + 5 = 3a + 6$, Subtract $3a$ from both sides: $3a + 5 = 6$, Subtract $5$ from both sides: $3a = 1$, Solve for $a$: $a = \frac{1}{3}$.

Answer: $a = \frac{1}{3}$.

4. Solve $4(x - 7) = 0.3(x + 2) + 2.11$

• Expand: $4(x - 7) = 4x - 28$, $0.3(x + 2) = 0.3x + 0.6$, Equation becomes: $4x - 28 = 0.3x + 0.6 + 2.11$, Combine terms: $4x - 28 = 0.3x + 2.71$, Subtract $0.3x$ from both sides: $3.7x - 28 = 2.71$, Add $28$ to both sides: $3.7x = 30.71$, Solve for $x$: $x = \frac{30.71}{3.7} = 8.3$.

Answer: $x = 8.3$.

5. The solution to $4(x - 5) = x + 2$ (additional question inferred from layout)

Simplified quickly: $4x - 20 = x + 2$ → $3x = 22$ → $x = \frac{22}{3}$.

If you’d like detailed explanations for other questions, feel free to ask! Here are some related questions to expand your understanding:

1. Can you solve a similar equation with decimals or fractions?
2. How would you verify the solutions to equations?
3. Why is combining like terms important in solving equations?
4. What happens if we have no solution or infinite solutions?
5. How do we simplify complex fractions in equations?

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