We are given the inequality:

\[
15 \leq 3(a + 3) \leq 1
\]

This appears to involve two inequalities combined, so we will solve it step by step. First, let's break this into two parts:

### Part 1: Solve \( 15 \leq 3(a + 3) \)

1. Start by expanding the right-hand side:
   \[
   15 \leq 3a + 9
   \]

2. Subtract 9 from both sides:
   \[
   6 \leq 3a
   \]

3. Divide both sides by 3:
   \[
   2 \leq a
   \]
   or equivalently:
   \[
   a \geq 2
   \]

### Part 2: Solve \( 3(a + 3) \leq 1 \)

1. Expand the left-hand side:
   \[
   3a + 9 \leq 1
   \]

2. Subtract 9 from both sides:
   \[
   3a \leq -8
   \]

3. Divide both sides by 3:
   \[
   a \leq -\frac{8}{3}
   \]

### Conclusion

Now, we combine the two results from both parts:

- From Part 1: \( a \geq 2 \)
- From Part 2: \( a \leq -\frac{8}{3} \)

Since there is no value of \( a \) that satisfies both conditions at the same time, the inequality has **no solution**.

Would you like more details or have any questions?

### Related questions:
1. What happens if we change the constants in the inequality?
2. How would the solution change if we only had one inequality?
3. Can this inequality system have a graphical interpretation?
4. How do we solve compound inequalities in general?
5. What would the solution look like if we changed the inequality signs?

### Tip:
When solving compound inequalities, always solve each part separately and then combine the results carefully to find the correct solution set.

Discover how to solve the compound inequality 15 ≤ 3(a + 3) ≤ 1. This detailed solution walks through breaking down and solving each part of the inequality step by step, explaining key algebraic concepts like inequalities and inequality properties. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation