We will solve the equation \(-4x - 10 = 2x + 14\) step by step.

### Step 1: Move the terms involving \(x\) to one side.
To do this, subtract \(2x\) from both sides:
\[
-4x - 10 - 2x = 2x + 14 - 2x
\]
\[
-6x - 10 = 14
\]

### Step 2: Move the constant terms to the other side.
Add 10 to both sides:
\[
-6x - 10 + 10 = 14 + 10
\]
\[
-6x = 24
\]

### Step 3: Solve for \(x\).
To isolate \(x\), divide both sides by \(-6\):
\[
x = \frac{24}{-6}
\]
\[
x = -4
\]

### Final Answer: 
The solution to the equation is \(x = -4\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the equation was \( -4x - 10 = 3x + 14 \)?
2. What happens if you switch the sign of all terms in the equation?
3. How can we verify that \(x = -4\) is the correct solution?
4. How do we approach similar equations with fractions?
5. How do we solve the equation if the terms were quadratic, like \( -4x^2 - 10 = 2x + 14 \)?

**Tip**: Always aim to simplify the equation by isolating the variable step by step, keeping operations balanced across both sides!

Discover how to solve the linear equation -4x - 10 = 2x + 14 with this detailed step-by-step solution. This guide covers key algebra concepts like isolating variables, moving terms, and solving for x. Suitable for students in Grades 6-8.

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