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Let's solve the compound inequality step by step:

### Inequality 1:
\[
3x + 3 < 21
\]
1. Subtract 3 from both sides:
   \[
   3x < 18
   \]
2. Divide both sides by 3:
   \[
   x < 6
   \]

### Inequality 2:
\[
4x + 6 \leq -10
\]
1. Subtract 6 from both sides:
   \[
   4x \leq -16
   \]
2. Divide both sides by 4:
   \[
   x \leq -4
   \]

### Compound Inequality:
The compound inequality is joined by an **"and"**, which means we need to find the intersection of the solutions from both inequalities.

- From the first inequality, we have \( x < 6 \).
- From the second inequality, we have \( x \leq -4 \).

The intersection of these two inequalities is:
\[
x \leq -4
\]

### Interval Notation:
The solution in interval notation is:
\[
(-\infty, -4]
\]

Would you like further details or have any questions? Here are some related problems to explore:

1. How do you solve compound inequalities that involve "or" instead of "and"?
2. What are the steps for solving absolute value inequalities?
3. Can you explain how to graph compound inequalities on a number line?
4. How does solving inequalities differ from solving equations?
5. How do you solve compound inequalities involving three parts, such as \( a < x < b \)?

**Tip:** Always pay attention to whether the compound inequality uses "and" or "or," as this changes the solution method (intersection vs. union).

Solve the compound inequality: 3x + 3 < 21 and 4x + 6 ≤ -10

Learn how to solve the compound inequality 3x + 3 < 21 and 4x + 6 ≤ -10 step by step. This problem covers important algebraic concepts, including simplifying inequalities and finding intersections. Suitable for students in Grades 7-9.

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