The given equation is:

$3x - 5 = -x + 7$

Step 1: Move all terms involving $x$ to one side

Add $x$ to both sides:

$3x + x - 5 = 7$

$4x - 5 = 7$

Step 2: Isolate $x$

Add 5 to both sides:

$4x = 12$

Step 3: Solve for $x$

Divide by 4:

$x = \frac{12}{4} = 3$

Final Answer:

$x = 3$

Would you like a detailed explanation of any step?

Here are five related questions to explore further:

1. How do you check if your solution for $x$ is correct?
2. What happens if the equation has no solution?
3. How would the solution change if the equation were $3x - 5 = -x - 7$?
4. Can you solve an equation with fractions, such as $\frac{3x}{2} - 5 = -x + 7$?
5. How do you solve equations where $x$ appears in the denominator, like $\frac{3}{x} - 5 = -x + 7$?

Tip: Always check your solution by substituting the value of $x$ back into the original equation.