–
4≤2–
p
3
<
2
5
Write your answer as a compound inequality with integers, decimals, or proper or improper fractions in simplest form.



We are given the inequality:

\[
4 \leq 2 - \frac{p}{3} < \frac{2}{5}
\]

We will solve this as a compound inequality in two parts:

### Part 1: Solving \( 4 \leq 2 - \frac{p}{3} \)

1. Subtract 2 from both sides:

\[
4 - 2 \leq -\frac{p}{3}
\]

\[
2 \leq -\frac{p}{3}
\]

2. Multiply both sides by \(-3\) (and reverse the inequality):

\[
2 \times (-3) \geq p
\]

\[
-6 \geq p
\]

### Part 2: Solving \( 2 - \frac{p}{3} < \frac{2}{5} \)

1. Subtract 2 from both sides:

\[
2 - 2 - \frac{p}{3} < \frac{2}{5} - 2
\]

\[
-\frac{p}{3} < \frac{2}{5} - \frac{10}{5}
\]

\[
-\frac{p}{3} < -\frac{8}{5}
\]

2. Multiply both sides by \(-3\) (and reverse the inequality):

\[
p > \frac{24}{5}
\]

### Compound Inequality:

Now combine both parts of the inequality:

\[
\frac{24}{5} < p \leq -6
\]

This is the solution written as a compound inequality.

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Would you like more details on any part of the solution?

### Related Questions:
1. How do you reverse inequalities when multiplying by a negative number?
2. What are compound inequalities and how are they solved?
3. How do you handle fractions within inequalities?
4. Can inequalities have non-integer solutions?
5. How does solving a compound inequality differ from solving a system of inequalities?

**Tip**: Always be cautious when multiplying or dividing inequalities by negative numbers, as it reverses the inequality sign.

4 ≤ 2 - p/3 < 2/5. Write your answer as a compound inequality with integers, decimals, or proper or improper fractions in simplest form.

Learn how to solve the compound inequality 4 ≤ 2 - p/3 < 2/5 by breaking it into two parts and simplifying the inequality. This problem involves subtracting and multiplying fractions, as well as reversing inequalities when multiplying by a negative number. Suitable for students in Grades 8-10.

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