Let's solve the equation \(-6x - 7 = 2(2x - 1)\).

### Step 1: Expand the right-hand side
Distribute the \(2\) on the right-hand side:
\[
-6x - 7 = 4x - 2
\]

### Step 2: Move all terms involving \(x\) to one side
Add \(6x\) to both sides to move the \(x\) terms to the right-hand side:
\[
-7 = 4x + 6x - 2
\]
\[
-7 = 10x - 2
\]

### Step 3: Move the constant term to the other side
Add \(2\) to both sides to move the constant term to the left-hand side:
\[
-7 + 2 = 10x
\]
\[
-5 = 10x
\]

### Step 4: Solve for \(x\)
Divide both sides by \(10\) to isolate \(x\):
\[
x = \frac{-5}{10}
\]
\[
x = -\frac{1}{2}
\]

The solution is \(x = -\frac{1}{2}\).

Would you like more details or have any questions?

Here are some related questions:
1. How would the solution change if the equation had been \(-6x - 7 = 3(2x - 1)\)?
2. What happens if the constant term on the right-hand side is different?
3. Can you solve a similar equation where both sides have quadratic terms?
4. How can you check if the solution to a linear equation is correct?
5. What are the implications of having no solution or infinitely many solutions in such equations?

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

Learn how to solve the linear equation -6x - 7 = 2(2x - 1) step-by-step with detailed explanations. This problem involves basic algebraic concepts such as solving linear equations and using the distributive property. Suitable for students in Grades 7-9.

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