1. The problem is to solve the equation $$\frac{x+7}{6} = 1$$. 2. To solve for $x$, multiply both sides by 6 to cancel the denominator: $$6 \times \frac{x+7}{6} = 6 \times 1$$ 3. Using the cancellation rule: $$\cancel{6} \times \frac{x+7}{\cancel{6}} = 6$$ which simplifies to: $$x + 7 = 6$$ 4. Subtract 7 from both sides to isolate $x$: $$x + 7 - 7 = 6 - 7$$ $$x = -1$$ 5. The solution is $x = -1$. --- 2. The problem is to solve the equation $$\frac{x+7}{27} = 8 \times 4 - 3$$ with $x = -3$ given. 3. First, simplify the right side: $$8 \times 4 - 3 = 32 - 3 = 29$$ 4. Multiply both sides by 27: $$27 \times \frac{x+7}{27} = 27 \times 29$$ 5. Cancel 27: $$\cancel{27} \times \frac{x+7}{\cancel{27}} = 783$$ which simplifies to: $$x + 7 = 783$$ 6. Subtract 7: $$x = 783 - 7 = 776$$ 7. The given $x = -3$ does not satisfy this equation, so the correct solution is $x = 776$. --- 3. The problem is to solve $$\frac{x+2}{11} = 2$$. 4. Multiply both sides by 11: $$11 \times \frac{x+2}{11} = 11 \times 2$$ 5. Cancel 11: $$\cancel{11} \times \frac{x+2}{\cancel{11}} = 22$$ which simplifies to: $$x + 2 = 22$$ 6. Subtract 2: $$x = 22 - 2 = 20$$ 7. The solution is $x = 20$. --- 4. The problem is to solve $$\frac{x+7}{6} = 1$$ (repeated). 5. Multiply both sides by 6: $$6 \times \frac{x+7}{6} = 6 \times 1$$ 6. Cancel 6: $$\cancel{6} \times \frac{x+7}{\cancel{6}} = 6$$ which simplifies to: $$x + 7 = 6$$ 7. Subtract 7: $$x = 6 - 7 = -1$$ 8. The solution is $x = -1$. --- 5. The problem is to solve $$\frac{8 + x}{6} = 3$$. 6. Multiply both sides by 6: $$6 \times \frac{8 + x}{6} = 6 \times 3$$ 7. Cancel 6: $$\cancel{6} \times \frac{8 + x}{\cancel{6}} = 18$$ which simplifies to: $$8 + x = 18$$ 8. Subtract 8: $$x = 18 - 8 = 10$$ 9. The solution is $x = 10$. --- 13. The problem is to solve $$-6x + 8 = 110$$. 14. Subtract 8 from both sides: $$-6x + 8 - 8 = 110 - 8$$ $$-6x = 102$$ 15. Divide both sides by $-6$: $$\frac{-6x}{-6} = \frac{102}{-6}$$ 16. Cancel $-6$: $$\cancel{-6} x / \cancel{-6} = -17$$ which simplifies to: $$x = -17$$ --- 14. The problem is to solve $$5 + x = 4$$. 15. Subtract 5 from both sides: $$5 + x - 5 = 4 - 5$$ $$x = -1$$ 16. The solution is $x = -1$. --- 15. The problem is to solve $$\frac{x+7}{27} = 8 \times 4 - 3$$ with $x = -3$ given (same as problem 2, repeated). The solution is $x = 776$ as shown above. --- 16. The problem is to solve $$\frac{8 + x}{6} = 3$$ (same as problem 5, repeated). The solution is $x = 10$ as shown above.