1. **State the problem:** Simplify the expression $5\frac{a}{b}x - 3 + 3\frac{a}{b}x + 7 + 1\frac{a}{b}2$. 2. **Rewrite mixed fractions as improper fractions:** - $5\frac{a}{b}x = 5x + \frac{a}{b}x$ - $3\frac{a}{b}x = 3x + \frac{a}{b}x$ - $1\frac{a}{b}2 = 1 + \frac{a}{b} \times 2$ 3. **Substitute back:** $$5x + \frac{a}{b}x - 3 + 3x + \frac{a}{b}x + 7 + 1 + \frac{2a}{b}$$ 4. **Group like terms:** - Combine $x$ terms: $5x + 3x = 8x$ - Combine $\frac{a}{b}x$ terms: $\frac{a}{b}x + \frac{a}{b}x = 2\frac{a}{b}x$ - Combine constants: $-3 + 7 + 1 = 5$ - Add $\frac{2a}{b}$ as constant term 5. **Final simplified expression:** $$8x + 2\frac{a}{b}x + 5 + \frac{2a}{b}$$ 6. **Optional factorization:** Factor $x$ terms: $$x\left(8 + 2\frac{a}{b}\right) + 5 + \frac{2a}{b}$$ This is the simplified form of the original expression.