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!