To solve the equation \(-6x - 30 = 2x + 10\), follow these steps:

### Step 1: Move all terms involving \(x\) to one side of the equation.
To do this, add \(6x\) to both sides:
\[
-6x - 30 + 6x = 2x + 10 + 6x
\]
This simplifies to:
\[
-30 = 8x + 10
\]

### Step 2: Move the constant term to the other side.
Subtract 10 from both sides:
\[
-30 - 10 = 8x + 10 - 10
\]
Simplifying:
\[
-40 = 8x
\]

### Step 3: Solve for \(x\).
Now, divide both sides by 8:
\[
x = \frac{-40}{8}
\]
Simplifying:
\[
x = -5
\]

### Solution:
The solution to the equation is \(x = -5\).

Would you like any further details or clarification?

Here are five related questions to expand your understanding:
1. How would you solve the equation if the constants were different?
2. Can you verify the solution by substituting \(x = -5\) back into the original equation?
3. What happens when the variables are on the same side of the equation initially?
4. How would you handle the equation if there were fractions instead of integers?
5. What is the effect of dividing or multiplying both sides by a negative number?

**Tip:** When solving equations, always aim to isolate the variable by performing inverse operations step by step.

Learn how to solve the linear equation -6x - 30 = 2x + 10 with this detailed step-by-step guide. This solution covers fundamental algebra concepts such as moving terms, combining like terms, and solving for variables. Suitable for students in Grades 7-9.

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