Let's solve and verify the equation step by step:

Given equation:
\[
-\frac{1}{2}(x - (-4)) = -\frac{1}{2}x + 2
\]

### Step 1: Simplify the left-hand side
First, recognize that subtracting \(-4\) is the same as adding \(4\):
\[
-\frac{1}{2}(x + 4)
\]

Distribute \(-\frac{1}{2}\) to both terms inside the parentheses:
\[
-\frac{1}{2}x - 2
\]

So, the equation becomes:
\[
-\frac{1}{2}x - 2 = -\frac{1}{2}x + 2
\]

### Step 2: Compare both sides of the equation
Both sides of the equation have \(-\frac{1}{2}x\), so cancel them out:
\[
-2 = 2
\]

### Conclusion:
The equation results in a contradiction (\(-2\) does not equal \(2\)). Therefore, the original equation has **no solution**.

Would you like more details or have any questions?

Here are some related questions:
1. What is the significance of a contradiction in solving equations?
2. How do you solve linear equations with one variable?
3. What is the role of distribution in simplifying equations?
4. How do you identify when an equation has no solution?
5. Can you always cancel out terms on both sides of an equation?

**Tip:** Always check your equation step by step to catch any contradictions early on.

Learn how to solve the linear equation -1/2(x - (-4)) = -1/2x + 2 step-by-step with detailed explanations. Understand the distributive property and how to simplify equations involving fractions. Suitable for students in Grades 7-9.

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