1. The problem is to solve the inequality $$3|u| + 2 > 29$$ for the variable $$u$$. 2. Begin by isolating the absolute value term. $$3|u| + 2 > 29$$ Subtract 2 from both sides: $$3|u| > 27$$ 3. Divide both sides by 3: $$|u| > 9$$ 4. Recall that $$|u| > 9$$ means the value of $$u$$ is more than 9 units away from 0 on the number line. This translates to two cases: - $$u > 9$$ - $$u < -9$$ 5. Thus the solution can be written as a compound inequality: $$u < -9 \text{ or } u > 9$$ This is the final solution for $$u$$.