1. **State the problem:** Solve the inequality $3x + 4 < 7x + 24$. 2. **Write down the inequality:** $$3x + 4 < 7x + 24$$ 3. **Isolate the variable terms on one side:** Subtract $3x$ from both sides: $$4 < 7x - 3x + 24$$ Simplify: $$4 < 4x + 24$$ 4. **Isolate the constant terms on the other side:** Subtract $24$ from both sides: $$4 - 24 < 4x$$ Simplify: $$-20 < 4x$$ 5. **Solve for $x$ by dividing both sides by 4:** Since 4 is positive, the inequality direction stays the same: $$\frac{-20}{4} < x$$ Simplify: $$-5 < x$$ 6. **Rewrite the solution:** $$x > -5$$ **Answer:** The solution to the inequality is all $x$ such that $x > -5$. This means any number greater than $-5$ satisfies the inequality $3x + 4 < 7x + 24$.