1. **State the problem:** We need to find which of the given equations have no solution. 2. **Recall:** An equation has no solution if, after simplification, it results in a contradiction like $a = b$ where $a \neq b$ (e.g., $5 = 3$). 3. **Analyze each equation:** **Equation 1:** $2 + 4(4x + 5) = 8x + 2x - 11$ Expand left side: $2 + 16x + 20 = 18x - 11$ Simplify left: $16x + 22 = 18x - 11$ Bring variables to one side: $22 + 16x - 18x = -11$ $22 - 2x = -11$ Subtract 22: $-2x = -33$ Divide by $-2$: $x = \frac{33}{2}$ **Solution exists.** **Equation 2:** $-x + 3x - 7 = 2(x - 7)$ Simplify left: $2x - 7 = 2x - 14$ Subtract $2x$ both sides: $-7 = -14$ This is a contradiction. **No solution.** **Equation 3:** $7 - 5x(-3) = 5(3x - 2)$ Simplify left: $7 + 15x = 15x - 10$ Subtract $15x$ both sides: $7 = -10$ Contradiction. **No solution.** **Equation 4:** $6x + 3(2x - 1) = 5x - 4 + 7x + 1$ Expand left: $6x + 6x - 3 = 12x - 3$ Simplify right: $5x + 7x - 4 + 1 = 12x - 3$ Both sides equal $12x - 3$ This means infinite solutions, not no solution. 4. **Final answer:** Equations 2 and 3 have no solution.