Let's solve the equation step by step, following the guidance from the image.

We have the equation:

$3x + 7 = x + 1$

Step 1: Move all the terms with $x$ to one side.

We want to move all terms with $x$ to the left-hand side. So, subtract $x$ from both sides:

$3x - x + 7 = 1$

This simplifies to:

$2x + 7 = 1$

Step 2: Move constant terms to the other side.

Now, subtract 7 from both sides to move the constant to the right-hand side:

$2x = 1 - 7$

This simplifies to:

$2x = -6$

Step 3: Solve for $x$.

To solve for $x$, divide both sides by 2:

$x = \frac{-6}{2}$

This simplifies to:

$x = -3$

Final Answer:

$x = -3$

This is the correct solution. Would you like further details or clarification on any step?

Here are five related questions:

1. How can we check if the solution $x = -3$ is correct?
2. What would happen if we incorrectly moved terms in step 1?
3. How do we solve for $x$ if fractions are involved?
4. Can this equation have more than one solution?
5. How do you approach solving quadratic equations?

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