1. Problem 1: Solve for $x$ in the equation $$3(5x - 29) - 9 = -6$$ Step 1: Distribute 3 into terms inside parentheses: $$15x - 87 - 9 = -6$$ Step 2: Combine like terms on the left: $$15x - 96 = -6$$ Step 3: Add 96 to both sides: $$15x = 90$$ Step 4: Divide both sides by 15: $$x = \frac{90}{15} = 6$$ --- 2. Problem 2: Solve for $W$ in the equation $$-\frac{1}{2} + \frac{3}{8}W = -\frac{1}{3}$$ Step 1: Add $\frac{1}{2}$ to both sides to isolate the term with $W$: $$\frac{3}{8}W = -\frac{1}{3} + \frac{1}{2}$$ Step 2: Find a common denominator to combine the right side: Common denominator is 6: $$-\frac{2}{6} + \frac{3}{6} = \frac{1}{6}$$ Step 3: So we have: $$\frac{3}{8}W = \frac{1}{6}$$ Step 4: Multiply both sides by reciprocal of $\frac{3}{8}$ which is $\frac{8}{3}$: $$W = \frac{1}{6} \times \frac{8}{3} = \frac{8}{18} = \frac{4}{9}$$ --- 3. Problem 3: Solve for $V$ in the equation $$8.7V - 4.8 = -83.1$$ Step 1: Add 4.8 to both sides: $$8.7V = -83.1 + 4.8 = -78.3$$ Step 2: Divide both sides by 8.7: $$V = \frac{-78.3}{8.7} = -9$$ --- 4. Problem 4: Solve for $n$ in the equation $$-\frac{7}{8} = -\frac{2}{7}n$$ Step 1: Multiply both sides by reciprocal of $-\frac{2}{7}$ which is $-\frac{7}{2}$: $$n = -\frac{7}{8} \times -\frac{7}{2} = \frac{49}{16}$$ --- 5. Problem 5: Solve for $D$ in the equation $$-3 + D = \frac{4}{5}$$ Step 1: Add 3 to both sides: $$D = \frac{4}{5} + 3 = \frac{4}{5} + \frac{15}{5} = \frac{19}{5}$$