1. Solve $42 \div 3 = 18 - 41 \div 9$. Start by simplifying each division: $$42 \div 3 = 14$$ $$41 \div 9 \approx 4.555...$$ Rewrite the equation: $$14 = 18 - 4.555...$$ Calculate the right side: $$18 - 4.555... = 13.444...$$ Since $14 \neq 13.444...$, the original equation is false as stated. 2. Solve $-16 = -32 \div 2$. Simplify the division: $$-32 \div 2 = -16$$ So, $$-16 = -16$$ This is true. 3. Solve $-14 = \frac{x - 12}{-6}$. Multiply both sides by $-6$: $$-14 \times -6 = x - 12$$ $$84 = x - 12$$ Add 12 to both sides: $$84 + 12 = x$$ $$x = 96$$ 4. Solve $\frac{2}{3}x - 7 = 8$. Add 7 to both sides: $$\frac{2}{3}x = 8 + 7$$ $$\frac{2}{3}x = 15$$ Multiply both sides by $\frac{3}{2}$: $$x = 15 \times \frac{3}{2}$$ $$x = 22.5$$ 5. Solve $8x + (-2) = -9 + 7x$. Rewrite: $$8x - 2 = -9 + 7x$$ Subtract $7x$ from both sides: $$8x - 7x - 2 = -9$$ $$x - 2 = -9$$ Add 2 to both sides: $$x = -9 + 2$$ $$x = -7$$ 6. Solve $n + 2 = -4 + 2n$. Subtract $n$ from both sides: $$2 = -4 + n$$ Add 4 to both sides: $$2 + 4 = n$$ $$n = 6$$ 7. Solve $8(-5 + v) = 96$. Divide both sides by 8: $$-5 + v = \frac{96}{8}$$ $$-5 + v = 12$$ Add 5 to both sides: $$v = 12 + 5$$ $$v = 17$$ 8. Solve $-201 = -3 + 4(-4x - 3)$. Distribute 4: $$-201 = -3 + (-16x - 12)$$ Simplify right side: $$-201 = -3 - 16x - 12$$ $$-201 = -16x - 15$$ Add 15 to both sides: $$-201 + 15 = -16x$$ $$-186 = -16x$$ Divide both sides by $-16$: $$x = \frac{-186}{-16}$$ $$x = \frac{186}{16} = 11.625$$ 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: $$-10 - 58 = 31x$$ $$-68 = 31x$$ Divide both sides by 31: $$x = \frac{-68}{31} \approx -2.1935$$ 10. Solve $3q + 1 - 5 = -16 + 6q$. Simplify left side: $$3q - 4 = -16 + 6q$$ Subtract $3q$ from both sides: $$-4 = -16 + 3q$$ Add 16 to both sides: $$-4 + 16 = 3q$$ $$12 = 3q$$ Divide both sides by 3: $$q = 4$$