Let's solve the equation:

\[
-6x - 4 = \frac{1}{2}x - 4
\]

### Step 1: Eliminate the constant term on both sides.
Start by adding 4 to both sides to cancel the \(-4\):

\[
-6x - 4 + 4 = \frac{1}{2}x - 4 + 4
\]

This simplifies to:

\[
-6x = \frac{1}{2}x
\]

### Step 2: Eliminate the fraction.
To remove the fraction, multiply the entire equation by 2 (the denominator of the fraction):

\[
2(-6x) = 2\left(\frac{1}{2}x\right)
\]

This simplifies to:

\[
-12x = x
\]

### Step 3: Bring all \(x\) terms to one side.
Subtract \(x\) from both sides:

\[
-12x - x = 0
\]

This simplifies to:

\[
-13x = 0
\]

### Step 4: Solve for \(x\).
To find \(x\), divide both sides by \(-13\):

\[
x = 0
\]

### Final Answer:
\[
x = 0
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you solve equations with fractions more generally?
2. What happens if the solution isn't a whole number?
3. How do you handle equations with variables on both sides?
4. Can you apply these steps to an equation with exponents?
5. What if we need to solve inequalities instead of equations?

**Tip:** Always double-check your work by substituting the solution back into the original equation.

Learn how to solve the linear equation -6x - 4 = 1/2x - 4 step by step. This problem demonstrates algebraic techniques like balancing equations, eliminating fractions, and isolating variables. Suitable for students in Grades 8-10.

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