To solve the equation \( 4x + 1 = 2x + 7 \), follow these steps:

1. Subtract \( 2x \) from both sides:
   \[
   4x - 2x + 1 = 7
   \]
   This simplifies to:
   \[
   2x + 1 = 7
   \]

2. Subtract 1 from both sides:
   \[
   2x = 6
   \]

3. Divide both sides by 2:
   \[
   x = 3
   \]

Thus, the solution is \( x = 3 \).

Would you like more details on any step, or do you have other questions?

Here are 5 related questions:
1. How would you solve \( 5x + 3 = 2x + 9 \)?
2. What happens when both sides have the same term in a linear equation?
3. Can you solve \( 4x - 5 = 3x + 2 \)?
4. What is the solution to \( 3x + 4 = 3x + 9 \)?
5. How can you check if a solution to a linear equation is correct?

**Tip:** Always isolate the variable on one side to solve for it effectively.

Learn how to solve the linear equation 4x + 1 = 2x + 7 with a detailed step-by-step guide. This problem involves key algebraic concepts such as combining like terms and isolating variables, suitable for students in Grades 6-8.

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