1. **State the problem:** Simplify the expression $4x \times -72$. 2. **Formula and rules:** Multiplying a variable term by a constant involves multiplying the constants and keeping the variable as is. 3. **Intermediate work:** $$4x \times -72 = (4 \times -72) x$$ $$= -288x$$ 4. **Explanation:** We multiply 4 by -72 to get -288, then attach the variable $x$ to the product. 5. **Final answer:** $$-288x$$