Let's solve the equation step-by-step:

$-3(w+1) + 7 = 4(w+1) - 7$

Step 1: Distribute the constants

Distribute $-3$ and $4$ across the parentheses.

$-3w - 3 + 7 = 4w + 4 - 7$

Step 2: Combine like terms

Now, combine the constants on both sides.

$-3w + 4 = 4w - 3$

Step 3: Move variables to one side

Add $3w$ to both sides to move all terms involving $w$ to one side:

$4 = 7w - 3$

Step 4: Move constants to the other side

Add $3$ to both sides to move the constants to the other side:

$7 = 7w$

Step 5: Solve for $w$

Now, divide both sides by 7 to isolate $w$:

$w = 1$

Final Answer:

$w = 1$

Would you like a detailed explanation of any specific step? Or do you have any other questions?

Further Questions:

1. What happens if we check the solution by substituting $w = 1$ back into the original equation?
2. How do you handle equations with multiple variables or exponents?
3. What are some common mistakes made when solving linear equations?
4. Can you explain how to solve an equation with absolute value terms?
5. How do you solve a system of linear equations?

Tip:

Always distribute terms correctly and combine like terms to simplify equations before trying to solve them!