Solve Two Step 223E99

1. **State the problem:** Solve the two-step equation $$-4 = \frac{8}{9} (u - 3)$$ for $u$. 2. **Isolate the term with $u$:** To get rid of the fraction $$\frac{8}{9}$$, multiply both sides of the equation by its reciprocal $$\frac{9}{8}$$. $$-4 = \frac{8}{9} (u - 3)$$ Multiply both sides by $$\frac{9}{8}$$: $$\frac{9}{8} \times -4 = \frac{9}{8} \times \frac{8}{9} (u - 3)$$ 3. **Simplify both sides:** $$\frac{9}{8} \times -4 = -\frac{36}{8} = -\frac{9}{2}$$ On the right side, the $$\frac{9}{8}$$ and $$\frac{8}{9}$$ cancel out: $$\frac{9}{8} \times \frac{8}{9} = \cancel{\frac{9}{8}} \times \cancel{\frac{8}{9}} = 1$$ So the equation becomes: $$-\frac{9}{2} = u - 3$$ 4. **Solve for $u$:** Add 3 to both sides to isolate $u$: $$-\frac{9}{2} + 3 = u - 3 + 3$$ $$-\frac{9}{2} + 3 = u$$ 5. **Simplify the left side:** Convert 3 to a fraction with denominator 2: $$3 = \frac{6}{2}$$ So: $$-\frac{9}{2} + \frac{6}{2} = -\frac{3}{2}$$ 6. **Final answer:** $$u = -\frac{3}{2}$$