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Here are the solutions for the inequalities:

**(a) \( 5(6 - u) + 7u > 34 \):**
- The solution is \( u > 2 \). This means the inequality holds for all values of \( u \) greater than 2.

**(b) \( -3(v + 4) + 24 \leq 3(5 - v) \):**
- This inequality simplifies to a false statement (no valid solution). Hence, there is **no solution** for this inequality.

Would you like further details or clarification? Here are some related questions:

1. How do you solve inequalities with variables on both sides?
2. What does it mean when an inequality has no solution?
3. How can inequalities be represented graphically?
4. What are the rules for solving inequalities when multiplying or dividing by negative numbers?
5. How do you combine inequalities into a single expression?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

For each inequality, choose the statement that describes its solution. If applicable, give the solution.

Learn how to solve the inequalities 5(6 - u) + 7u > 34 and -3(v + 4) + 24 ≤ 3(5 - v). The solution for the first inequality is u > 2, while the second inequality has no solution. This topic covers key algebraic techniques for solving linear inequalities. Suitable for students in Grades 7-9.

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