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

1. **Move the variable terms to one side:**
   Subtract \( 3x \) from both sides:
   \[
   5x - 3x + 7 = -5
   \]
   This simplifies to:
   \[
   2x + 7 = -5
   \]

2. **Move the constant terms to the other side:**
   Subtract 7 from both sides:
   \[
   2x = -5 - 7
   \]
   Simplifying this:
   \[
   2x = -12
   \]

3. **Solve for \( x \):**
   Divide both sides by 2:
   \[
   x = \frac{-12}{2}
   \]
   This gives:
   \[
   x = -6
   \]

So, the solution is \( x = -6 \).

Would you like more details or explanations on any step?

Here are 5 related questions:
1. What happens if we start by subtracting \( 7 \) from both sides first?
2. How do we check if \( x = -6 \) is the correct solution?
3. Can you try solving \( 6x + 10 = 2x - 8 \)?
4. What if the equation had a fraction, like \( \frac{5x}{2} + 7 = 3x - 5 \)?
5. How do we solve \( 5x + 7 = 3x + c \), where \( c \) is a constant?

**Tip:** Always check your final solution by substituting it back into the original equation to verify.

Learn how to solve the linear equation 5x + 7 = 3x - 5 with a step-by-step solution. This problem covers key algebraic concepts, including moving terms across the equal sign and solving for x. Ideal for students in Grades 6-8.

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