We are solving the equation:

\[
2x + 1 = -x + 7
\]

### Step 1: Combine like terms.
Move \(-x\) to the left side by adding \(x\) to both sides:

\[
2x + x + 1 = 7
\]

This simplifies to:

\[
3x + 1 = 7
\]

### Step 2: Isolate the variable term.
Subtract 1 from both sides:

\[
3x = 6
\]

### Step 3: Solve for \(x\).
Divide both sides by 3:

\[
x = 2
\]

So, the solution is:

\[
x = 2
\]

Would you like more details, or do you have any questions about this process?

Here are 5 related questions:
1. How do you solve equations with fractions?
2. What happens if the equation has variables on both sides?
3. How can you solve equations with exponents?
4. What are linear equations, and how are they solved?
5. How do you solve systems of equations with two variables?

**Tip:** Always perform the same operation on both sides of the equation to maintain equality!

Learn how to solve the linear equation 2x + 1 = -x + 7 step-by-step. This problem demonstrates the fundamental concept of solving linear equations and applying the equality property of equations. Suitable for students in Grades 6-8.

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