Let's solve the equation step by step:

Given equation:
\[
-4x - 4 = -4(x + 2)
\]

### Step 1: Expand the right-hand side
Distribute the \(-4\) on the right-hand side:
\[
-4x - 4 = -4x - 8
\]

### Step 2: Eliminate like terms
Now, subtract \(-4x\) from both sides:
\[
-4 = -8
\]

This is a contradiction because \(-4 \neq -8\). Therefore, the equation has **no solution**.

Would you like further details or have any questions?

Here are 5 related questions to practice:
1. Solve for \( x \): \( 3x + 5 = 3(x + 2) \)
2. Solve for \( x \): \( 2x + 7 = 3(x + 1) \)
3. Solve for \( x \): \( 5(x - 1) = 5x - 5 \)
4. Solve for \( x \): \( -6x - 12 = -6(x + 3) \)
5. Solve for \( x \): \( 7(x - 2) = 7x - 14 \)

**Tip**: Always simplify both sides of an equation before trying to isolate the variable. This helps catch any contradictions or special cases early!

Discover how to solve the equation −4x − 4 = −4(x + 2), which leads to a contradiction, indicating no solution. This problem involves algebraic concepts such as the distributive property and recognizing contradictions. Suitable for students in Grades 8-10.

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