1. **State the problem:** Solve the inequality $5x + 3 < 2x - 1$. 2. **Write the inequality:** $$5x + 3 < 2x - 1$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$5x + 3 - 2x < 2x - 1 - 2x$$ $$\cancel{5x} + 3 - \cancel{2x} < \cancel{2x} - 1 - \cancel{2x}$$ $$3x + 3 < -1$$ 4. **Isolate the constant terms on the other side:** Subtract $3$ from both sides: $$3x + 3 - 3 < -1 - 3$$ $$3x + \cancel{3} - \cancel{3} < -4$$ $$3x < -4$$ 5. **Solve for $x$ by dividing both sides by 3:** Since 3 is positive, the inequality direction stays the same: $$\frac{3x}{3} < \frac{-4}{3}$$ $$x < -\frac{4}{3}$$ **Final answer:** $$x < -\frac{4}{3}$$ This means all values of $x$ less than $-\frac{4}{3}$ satisfy the inequality.