1. **State the problem:** Calculate the value of $7 \times \left(1 \frac{5}{7}\right) + 2$ and compare it to $9 + 5$. 2. **Convert the mixed number to an improper fraction:** $$1 \frac{5}{7} = \frac{7}{7} + \frac{5}{7} = \frac{12}{7}$$ 3. **Multiply 7 by the improper fraction:** $$7 \times \frac{12}{7}$$ 4. **Simplify the multiplication by canceling the 7 in numerator and denominator:** $$\cancel{7} \times \frac{12}{\cancel{7}} = 12$$ 5. **Add 2 to the result:** $$12 + 2 = 14$$ 6. **Calculate the right side of the equation:** $$9 + 5 = 14$$ 7. **Compare both sides:** Both sides equal 14, so the equation holds true. **Final answer:** $14$