1. **Stating the problem:** Simplify the expression $7 - 1 \frac{5}{6} x - 2 \frac{1}{7}$ and verify the steps given. 2. **Convert mixed numbers to improper fractions:** - $1 \frac{5}{6} = \frac{11}{6}$ - $2 \frac{1}{7} = \frac{15}{7}$ 3. **Rewrite the expression:** $$7 - \frac{11}{6} x - \frac{15}{7}$$ 4. **Check the intermediate step given:** The user wrote $-\frac{14}{6} x - \frac{15}{7}$ which seems to be a simplification step. Let's verify if $7 - \frac{11}{6} x$ equals $-\frac{14}{6} x$. 5. **Clarify the expression:** It appears the user is trying to simplify or solve an equation but the expression is ambiguous. Assuming the expression is $7 - \frac{11}{6} x - \frac{15}{7}$, combine constants: 6. **Find common denominator for constants $7$ and $-\frac{15}{7}$:** $$7 = \frac{49}{7}$$ So, $$\frac{49}{7} - \frac{15}{7} = \frac{34}{7}$$ 7. **Rewrite expression:** $$\frac{34}{7} - \frac{11}{6} x$$ 8. **Final simplified form:** $$\frac{34}{7} - \frac{11}{6} x$$ Since the user also wrote $= \frac{10}{3} = 3 \frac{1}{3}$, it seems they evaluated the expression for some $x$ value, but it is unclear. **Summary:** The expression simplifies to $$\frac{34}{7} - \frac{11}{6} x$$. --- **Second problem:** Simplify $5 \frac{2}{3} \div -1 \frac{2}{3}$. 1. Convert mixed numbers to improper fractions: $$5 \frac{2}{3} = \frac{17}{3}$$ $$-1 \frac{2}{3} = -\frac{5}{3}$$ 2. Division of fractions is multiplication by reciprocal: $$\frac{17}{3} \div -\frac{5}{3} = \frac{17}{3} \times -\frac{3}{5}$$ 3. Multiply numerators and denominators: $$= \frac{17 \times -3}{3 \times 5} = \frac{-51}{15}$$ 4. Simplify fraction by dividing numerator and denominator by 3: $$= \frac{\cancel{-51}^{-17}}{\cancel{15}^5} = -\frac{17}{5}$$ 5. Convert to mixed number: $$-\frac{17}{5} = -3 \frac{2}{5}$$ --- **Final answers:** - First expression simplified: $$\frac{34}{7} - \frac{11}{6} x$$ - Second expression evaluated: $$-3 \frac{2}{5}$$