We are given the equation:

\[
4(-4 - 4x) + 28x + 4x = -272
\]

### Step 1: Distribute the 4 on the left-hand side
\[
4(-4 - 4x) = 4 \times (-4) + 4 \times (-4x) = -16 - 16x
\]

So the equation becomes:
\[
-16 - 16x + 28x + 4x = -272
\]

### Step 2: Combine like terms
Combine all the terms involving \(x\):
\[
-16x + 28x + 4x = 16x
\]
So now the equation looks like:
\[
-16 + 16x = -272
\]

### Step 3: Solve for \(x\)
First, isolate the term with \(x\) by adding 16 to both sides:
\[
16x = -272 + 16
\]
\[
16x = -256
\]

Next, divide both sides by 16:
\[
x = \frac{-256}{16}
\]
\[
x = -16
\]

So the solution is:
\[
x = -16
\]

Would you like further details or explanations on any of the steps?

Here are five related questions:
1. How do you simplify expressions with variables?
2. What are the rules for distributing in algebra?
3. Can you explain how to solve multi-step equations?
4. What does it mean to combine like terms?
5. How do you check the solution of an equation?

**Tip**: When combining like terms, always ensure they have the same variable and exponent!

Learn how to solve the linear equation 4(−4−4x) + 28x + 4x = −272 with a detailed step-by-step guide. This problem focuses on using the distributive property and combining like terms. Suitable for students in Grades 8-10.

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