1. **State the problem:** Solve the inequality $5x + 3 > 2x - 7$. 2. **Recall the rule:** To solve inequalities, we isolate the variable on one side. When adding or subtracting terms, do the same on both sides. If multiplying or dividing by a negative number, reverse the inequality sign. 3. **Step 1:** Subtract $2x$ from both sides to get all $x$ terms on one side: $$5x + 3 - 2x > 2x - 7 - 2x$$ which simplifies to $$3x + 3 > -7$$ 4. **Step 2:** Subtract 3 from both sides to isolate the term with $x$: $$3x + 3 - 3 > -7 - 3$$ which simplifies to $$3x > -10$$ 5. **Step 3:** Divide both sides by 3 (a positive number, so inequality direction stays the same): $$x > \frac{-10}{3}$$ 6. **Final answer:** The solution to the inequality is $$x > -\frac{10}{3}$$ This means any $x$ greater than $-\frac{10}{3}$ satisfies the inequality.