1. **State the problem:** Solve for $a$ in the equation $2a + 0.8\overline{3} = 4.6\overline{6}$. 2. **Understand repeating decimals:** - $0.8\overline{3}$ means $0.8333\ldots$ - $4.6\overline{6}$ means $4.6666\ldots$ 3. **Convert repeating decimals to fractions:** - Let $x = 0.8\overline{3}$. Multiply by 10: $10x = 8.3\overline{3}$. Subtract original: $10x - x = 8.3\overline{3} - 0.8\overline{3} \Rightarrow 9x = 7.5$. So, $x = \frac{7.5}{9} = \frac{15}{18} = \frac{5}{6}$. - Let $y = 4.6\overline{6}$. Multiply by 10: $10y = 46.6\overline{6}$. Subtract original: $10y - y = 46.6\overline{6} - 4.6\overline{6} \Rightarrow 9y = 42$. So, $y = \frac{42}{9} = \frac{14}{3}$. 4. **Rewrite the equation with fractions:** $$2a + \frac{5}{6} = \frac{14}{3}$$ 5. **Isolate $a$:** $$2a = \frac{14}{3} - \frac{5}{6}$$ 6. **Find common denominator and subtract:** $$\frac{14}{3} = \frac{28}{6}$$ $$2a = \frac{28}{6} - \frac{5}{6} = \frac{23}{6}$$ 7. **Divide both sides by 2:** $$a = \frac{\frac{23}{6}}{2} = \frac{23}{6} \times \frac{1}{2} = \frac{23}{12}$$ 8. **Final answer:** $$a = \frac{23}{12}$$ or approximately $1.9167$. This means $a$ is $\frac{23}{12}$ which is a little less than 2.