Let's solve the inequality:

\[
-27x - 54 < 7(-3x - 4 - 4)
\]

### Step 1: Simplify the right-hand side
First, simplify the expression inside the parentheses on the right-hand side:

\[
-3x - 4 - 4 = -3x - 8
\]

Now, the inequality becomes:

\[
-27x - 54 < 7(-3x - 8)
\]

### Step 2: Distribute the 7 on the right-hand side

\[
7(-3x - 8) = 7(-3x) + 7(-8) = -21x - 56
\]

Now, the inequality is:

\[
-27x - 54 < -21x - 56
\]

### Step 3: Collect like terms
To simplify further, let's add \(21x\) to both sides:

\[
-27x + 21x - 54 < -21x + 21x - 56
\]

This simplifies to:

\[
-6x - 54 < -56
\]

### Step 4: Isolate the variable
Add 54 to both sides:

\[
-6x - 54 + 54 < -56 + 54
\]

\[
-6x < -2
\]

### Step 5: Solve for \(x\)
Now, divide both sides by \(-6\). Remember, dividing by a negative number reverses the inequality sign:

\[
x > \frac{-2}{-6}
\]

\[
x > \frac{1}{3}
\]

### Final Answer:

\[
x > \frac{1}{3}
\]

Would you like more details, or have any questions about the solution? 

Here are 5 related questions to consider:
1. How do you solve linear inequalities involving fractions?
2. What happens when multiplying or dividing an inequality by a negative number?
3. How do you represent the solution to an inequality on a number line?
4. How would the solution change if it were a greater than or equal inequality?
5. How do inequalities differ from equations in terms of graphing?

**Tip:** When solving inequalities, always reverse the inequality sign when multiplying or dividing by a negative number.

This step-by-step guide explains how to solve the linear inequality -27x - 54 < 7(-3x - 4 - 4), covering key algebraic concepts like the distributive property and the rule of inequalities. Suitable for students in Grades 9-11.

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