1. Solve $42 = 18 - 4t$. Subtract 18 from both sides: $$42 - 18 = 18 - 18 - 4t \Rightarrow 24 = -4t$$ Divide both sides by $-4$: $$\frac{24}{\cancel{-4}} = \frac{-4t}{\cancel{-4}} \Rightarrow -6 = t$$ 2. Solve $-16 = -32 - \frac{2}{5}f$. Add 32 to both sides: $$-16 + 32 = -32 + 32 - \frac{2}{5}f \Rightarrow 16 = -\frac{2}{5}f$$ Multiply both sides by $-\frac{5}{2}$ to isolate $f$: $$16 \times -\frac{5}{2} = f \Rightarrow -40 = f$$ 3. Solve $-14 = \frac{x - 12}{-6}$. Multiply both sides by $-6$: $$-14 \times \cancel{-6} = \frac{x - 12}{\cancel{-6}} \times \cancel{-6} \Rightarrow 84 = x - 12$$ Add 12 to both sides: $$84 + 12 = x - 12 + 12 \Rightarrow 96 = x$$ 4. Solve $\frac{2}{3}x - 7 = 8$. Add 7 to both sides: $$\frac{2}{3}x - 7 + 7 = 8 + 7 \Rightarrow \frac{2}{3}x = 15$$ Multiply both sides by $\frac{3}{2}$: $$\frac{3}{2} \times \frac{2}{3}x = 15 \times \frac{3}{2} \Rightarrow x = 22.5$$ 5. Solve $8x + (-2) = -9 + 7x$. Simplify left side: $$8x - 2 = -9 + 7x$$ Subtract $7x$ from both sides: $$8x - 7x - 2 = -9 + 7x - 7x \Rightarrow x - 2 = -9$$ Add 2 to both sides: $$x - 2 + 2 = -9 + 2 \Rightarrow x = -7$$ 6. Solve $n + 2 = -4 + 2n$. Subtract $n$ from both sides: $$n - n + 2 = -4 + 2n - n \Rightarrow 2 = -4 + n$$ Add 4 to both sides: $$2 + 4 = -4 + 4 + n \Rightarrow 6 = n$$ 7. Solve $8(-5 + v) = 96$. Distribute 8: $$8 \times -5 + 8v = 96 \Rightarrow -40 + 8v = 96$$ Add 40 to both sides: $$-40 + 40 + 8v = 96 + 40 \Rightarrow 8v = 136$$ Divide both sides by 8: $$\frac{8v}{\cancel{8}} = \frac{136}{\cancel{8}} \Rightarrow v = 17$$ 8. Solve $-201 = -3 + 4(-4x - 3)$. Distribute 4: $$-201 = -3 + 4 \times -4x + 4 \times -3 \Rightarrow -201 = -3 - 16x - 12$$ Combine like terms on right: $$-201 = -15 - 16x$$ Add 15 to both sides: $$-201 + 15 = -15 + 15 - 16x \Rightarrow -186 = -16x$$ Divide both sides by $-16$: $$\frac{-186}{\cancel{-16}} = \frac{-16x}{\cancel{-16}} \Rightarrow \frac{186}{16} = x$$ Simplify fraction: $$x = \frac{93}{8} = 11.625$$ 9. Solve $-10 = 4(6x + 4) + 7(x + 6)$. Distribute: $$-10 = 24x + 16 + 7x + 42$$ Combine like terms: $$-10 = 31x + 58$$ Subtract 58 from both sides: $$-10 - 58 = 31x + 58 - 58 \Rightarrow -68 = 31x$$ Divide both sides by 31: $$\frac{-68}{\cancel{31}} = \frac{31x}{\cancel{31}} \Rightarrow x = -\frac{68}{31} \approx -2.19$$ 10. Solve $3q + 1 - 5 = -16 + 6q$. Simplify left side: $$3q - 4 = -16 + 6q$$ Subtract $3q$ from both sides: $$3q - 3q - 4 = -16 + 6q - 3q \Rightarrow -4 = -16 + 3q$$ Add 16 to both sides: $$-4 + 16 = -16 + 16 + 3q \Rightarrow 12 = 3q$$ Divide both sides by 3: $$\frac{12}{\cancel{3}} = \frac{3q}{\cancel{3}} \Rightarrow q = 4$$