To solve the equation \( 7x + 3 = 5x + 1 \), follow these steps:

1. **Subtract \( 5x \) from both sides** to get all the \( x \)-terms on one side:
   \[
   7x + 3 - 5x = 5x + 1 - 5x
   \]
   Simplifying this gives:
   \[
   2x + 3 = 1
   \]

2. **Subtract 3 from both sides** to isolate the \( x \)-terms:
   \[
   2x + 3 - 3 = 1 - 3
   \]
   Simplifying this gives:
   \[
   2x = -2
   \]

3. **Divide both sides by 2** to solve for \( x \):
   \[
   \frac{2x}{2} = \frac{-2}{2}
   \]
   Simplifying this gives:
   \[
   x = -1
   \]

The solution to the equation \( 7x + 3 = 5x + 1 \) is \( x = -1 \).

Would you like any more details or have any questions?

Here are some related questions you might find interesting:

1. What happens if you change the constants in the equation, such as \( 7x + 3 = 5x + 2 \)?
2. How do you solve an equation where the variable \( x \) appears on one side only?
3. Can you solve the equation if it contains fractions, like \( \frac{7x}{2} + 3 = 5x + 1 \)?
4. How would you solve an equation with variables on both sides and multiple constants, such as \( 4x + 2 = 2x + 6 \)?
5. What are the steps to solve a quadratic equation like \( 3x^2 + 2x - 1 = 0 \)?

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

Learn how to solve the equation 7x + 3 = 5x + 1 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations and algebraic manipulation. Suitable for students in Grades 7-9.

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