1. **Problem 1:** Solve the equation $4^3 = 4(2x + 3)$. - Calculate $4^3 = 64$. - Set up the equation: $64 = 4(2x + 3)$. - Divide both sides by 4: $16 = 2x + 3$. - Subtract 3: $16 - 3 = 2x$ so $13 = 2x$. - Divide by 2: $x = \frac{13}{2}$. 2. **Problem 2:** Solve the equation $\frac{2}{3} = \frac{2m - 1}{3}$. - Multiply both sides by 3: $2 = 2m - 1$. - Add 1: $2 + 1 = 2m$ so $3 = 2m$. - Divide by 2: $m = \frac{3}{2}$. 3. **Problem 3:** Solve $1 - 8x = -5(-x + 2)$. - Expand right side: $-5(-x + 2) = 5x - 10$. - Equation becomes: $1 - 8x = 5x - 10$. - Add $8x$ to both sides: $1 = 13x - 10$. - Add 10: $11 = 13x$. - Divide by 13: $x = \frac{11}{13}$. 4. **Problem 4:** Simplify $\frac{-x + 4}{5 - 6x} \times \frac{2}{3}$. - Multiply numerators: $(-x + 4) \times 2 = -2x + 8$. - Multiply denominators: $(5 - 6x) \times 3 = 15 - 18x$. - Result: $\frac{-2x + 8}{15 - 18x}$. 5. **Problem 5:** Solve $4k = \frac{k}{2}$. - Multiply both sides by 2: $8k = k$. - Subtract $k$: $7k = 0$. - Divide by 7: $k = 0$. 6. **Problem 6:** Solve $-2(5 - 3x) = 4(2x + 3)$. - Expand both sides: $-10 + 6x = 8x + 12$. - Subtract $6x$: $-10 = 2x + 12$. - Subtract 12: $-22 = 2x$. - Divide by 2: $x = -11$. **Final answers:** - $x = \frac{13}{2}$ - $m = \frac{3}{2}$ - $x = \frac{11}{13}$ - Simplified expression: $\frac{-2x + 8}{15 - 18x}$ - $k = 0$ - $x = -11$