Question: Solve the following inequality:
1 > -3 \left( \frac{2}{3} x - 4 \right) - 1
1. **State the problem:** Solve the inequality $$1 > -3 \left( \frac{2}{3} x - 4 \right) - 1$$.
2. **Rewrite the inequality:**
$$1 > -3 \left( \frac{2}{3} x - 4 \right) - 1$$
3. **Add 1 to both sides to isolate the term with $x$:**
$$1 + 1 > -3 \left( \frac{2}{3} x - 4 \right)$$
$$2 > -3 \left( \frac{2}{3} x - 4 \right)$$
4. **Distribute $-3$ inside the parentheses:**
$$2 > -3 \times \frac{2}{3} x + (-3) \times (-4)$$
$$2 > -2x + 12$$
5. **Subtract 12 from both sides:**
$$2 - 12 > -2x + 12 - 12$$
$$-10 > -2x$$
6. **Divide both sides by $-2$ to solve for $x$.** Remember, dividing by a negative number reverses the inequality sign:
$$\frac{-10}{\cancel{-2}} \; \cancel{>} \; \frac{-2x}{\cancel{-2}}$$
$$5 < x$$
7. **Rewrite the solution:**
$$x > 5$$
**Final answer:** $$x > 5$$