1. **State the problem:** Solve the inequality $5x + 3 > 2x - 7$. 2. **Isolate the variable terms:** Subtract $2x$ from both sides to get all $x$ terms on one side. $$5x + 3 > 2x - 7$$ $$5x - \cancel{2x} + 3 > \cancel{2x} - 7$$ $$3x + 3 > -7$$ 3. **Isolate the constant terms:** Subtract 3 from both sides. $$3x + \cancel{3} > -7 - \cancel{3}$$ $$3x > -10$$ 4. **Solve for $x$:** Divide both sides by 3. $$\frac{3x}{\cancel{3}} > \frac{-10}{\cancel{3}}$$ $$x > -\frac{10}{3}$$ 5. **Interpretation:** The solution to the inequality is all $x$ values greater than $-\frac{10}{3}$. **Final answer:** $$x > -\frac{10}{3}$$