1. **State the problem:** Solve the equation $$\frac{4}{5}x + 3 = -\frac{7}{10}$$ for $x$. 2. **Isolate the term with $x$:** Subtract 3 from both sides: $$\frac{4}{5}x + 3 - 3 = -\frac{7}{10} - 3$$ $$\frac{4}{5}x = -\frac{7}{10} - \frac{30}{10}$$ $$\frac{4}{5}x = -\frac{37}{10}$$ 3. **Solve for $x$ by dividing both sides by $\frac{4}{5}$:** $$x = \frac{-\frac{37}{10}}{\frac{4}{5}}$$ 4. **Rewrite division as multiplication by reciprocal:** $$x = -\frac{37}{10} \times \frac{5}{4}$$ 5. **Multiply numerators and denominators:** $$x = -\frac{37 \times 5}{10 \times 4} = -\frac{185}{40}$$ 6. **Simplify the fraction by dividing numerator and denominator by 5:** $$x = -\frac{\cancel{185}^{37}}{\cancel{40}^{8}} = -\frac{37}{8}$$ **Final answer:** $$x = -\frac{37}{8}$$