Let's solve the equation $3x + 7 = x - 1$ step by step and check if $x = -4$ is a solution.

Step 1: Simplify the equation

Start with: $3x + 7 = x - 1$

Subtract $x$ from both sides: $3x - x + 7 = -1$ $2x + 7 = -1$

Step 2: Isolate $x$

Subtract 7 from both sides: $2x = -1 - 7$ $2x = -8$

Divide both sides by 2: $x = -4$

Step 3: Verify the solution

Substitute $x = -4$ back into the original equation: $3(-4) + 7 = -4 - 1$ $-12 + 7 = -5$ $-5 = -5$

The equation holds true, so $x = -4$ is indeed a solution.

Do you have any further questions or need additional details? Here are some related questions to deepen your understanding:

1. What are the general steps to solve linear equations like this one?
2. How can you verify the solution of an equation using substitution?
3. What is the significance of balancing operations when solving equations?
4. How would the process change if the equation were nonlinear (e.g., $x^2$ terms)?
5. Can this equation have more than one solution? Why or why not?

Tip: Always double-check your solution by substituting it back into the original equation to ensure accuracy.