We are tasked with solving the compound inequality:

\[
9 - 3 < 1 - 6x \leq 4
\]

### Step 1: Break the compound inequality into two parts.

1. \( 9 - 3 < 1 - 6x \)
2. \( 1 - 6x \leq 4 \)

---

### Step 2: Solve the first inequality \( 9 - 3 < 1 - 6x \).

\[
6 < 1 - 6x
\]
Subtract 1 from both sides:
\[
6 - 1 < -6x \implies 5 < -6x
\]
Now, divide by \(-6\), and since we are dividing by a negative number, we reverse the inequality:
\[
\frac{5}{-6} > x \implies x < -\frac{5}{6}
\]

---

### Step 3: Solve the second inequality \( 1 - 6x \leq 4 \).

Subtract 1 from both sides:
\[
-6x \leq 4 - 1 \implies -6x \leq 3
\]
Now, divide by \(-6\), and again reverse the inequality:
\[
x \geq -\frac{1}{2}
\]

---

### Step 4: Combine the results.

From the first inequality, we have \( x < -\frac{5}{6} \), and from the second inequality, \( x \geq -\frac{1}{2} \).

Since there is no overlap between these two conditions, there is **no solution** to this compound inequality.

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Would you like further details on any step or explanation?

Here are some related questions for further practice:

1. Solve the inequality: \( 7 - 2x \leq 3 + 5x \).
2. Solve the compound inequality: \( -2 \leq 3x - 4 \leq 

This step-by-step guide explains how to solve the compound inequality 9 - 3 < 1 - 6x <= 4. Learn the rules for handling compound inequalities, including reversing the inequality when dividing by a negative number. Suitable for students in Grades 9-10.

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