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Based on the clues, solve the equation with the steps.

Solve 3x + 7 = x + 1

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.

Learn how to solve the linear equation 3x + 7 = x + 1 with a step-by-step breakdown. This algebra problem focuses on moving terms, simplifying expressions, and solving for x. Suitable for students in Grades 7-9.

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