The uploaded image contains three multi-step equations to solve for the variable. I will solve each one step-by-step.

1) $2(x + 3) - 5 = 4x - 11$

Step 1: Distribute $2$ to the terms inside the parentheses: $2x + 6 - 5 = 4x - 11$

Step 2: Simplify the constants on the left side: $2x + 1 = 4x - 11$

Step 3: Move $2x$ to the right side by subtracting $2x$: $1 = 2x - 11$

Step 4: Add $11$ to both sides: $12 = 2x$

Step 5: Divide by $2$: $x = 6$

3) $5(z - 1) + 3z = 2(z + 4) + 9$

Step 1: Distribute $5$ and $2$: $5z - 5 + 3z = 2z + 8 + 9$

Step 2: Combine like terms: $8z - 5 = 2z + 17$

Step 3: Subtract $2z$ from both sides: $6z - 5 = 17$

Step 4: Add $5$ to both sides: $6z = 22$

Step 5: Divide by $6$: $z = \frac{22}{6} = \frac{11}{3}$

5) $3(2b + 1) - 4(b - 2) = 2b + 15$

Step 1: Distribute $3$ and $-4$: $6b + 3 - 4b + 8 = 2b + 15$

Step 2: Combine like terms on the left side: $2b + 11 = 2b + 15$

Step 3: Subtract $2b$ from both sides: $11 = 15$

Step 4: Identify contradiction: Since $11 \neq 15$, there is no solution to this equation. It is an inconsistent equation.

Final Answers:

1. $x = 6$
2. $z = \frac{11}{3}$
3. No solution

Would you like detailed explanations for any specific step?

Here are 5 related questions:

1. How do you identify inconsistent equations?
2. What happens if the variables cancel out but the constants are equal?
3. Can you solve similar equations involving fractions?
4. How would this process change for inequalities?
5. How do you check if a solution is correct?

Tip: Always distribute and simplify each side of the equation before moving terms!