1. **State the problem:** Simplify the expression $$2 \times \frac{4}{5} + \frac{14 + 3x}{4}$$. 2. **Apply multiplication:** Multiply 2 by the fraction $\frac{4}{5}$: $$2 \times \frac{4}{5} = \frac{2 \times 4}{5} = \frac{8}{5}$$ 3. **Rewrite the expression:** Now the expression is: $$\frac{8}{5} + \frac{14 + 3x}{4}$$ 4. **Find common denominator:** The denominators are 5 and 4. The least common denominator (LCD) is 20. 5. **Convert each fraction to have denominator 20:** $$\frac{8}{5} = \frac{8 \times 4}{5 \times 4} = \frac{32}{20}$$ $$\frac{14 + 3x}{4} = \frac{(14 + 3x) \times 5}{4 \times 5} = \frac{70 + 15x}{20}$$ 6. **Add the fractions:** $$\frac{32}{20} + \frac{70 + 15x}{20} = \frac{32 + 70 + 15x}{20} = \frac{102 + 15x}{20}$$ 7. **Simplify the fraction if possible:** Both numerator and denominator share a common factor of 1 only, so the fraction is already simplified. **Final answer:** $$\boxed{\frac{102 + 15x}{20}}$$