1. **State the problem:** Solve the inequality $x + 3 < -7$. 2. **Isolate the variable:** To solve for $x$, subtract 3 from both sides of the inequality. 3. **Show the subtraction step:** $$x + 3 - \cancel{3} < -7 - \cancel{3}$$ which simplifies to $$x < -10$$ 4. **Interpret the solution:** The solution to the inequality is all values of $x$ less than $-10$. 5. **Graph explanation:** On the number line, this is represented by a filled circle at $-10$ and an arrow pointing to the left, indicating all numbers less than $-10$ satisfy the inequality.