We can solve the equation $-7(w - 7) = -2x - 1$ step by step.

Step 1: Distribute the $-7$ on the left side of the equation:

$-7(w - 7) = -7w + 49$ So, the equation becomes: $-7w + 49 = -2x - 1$

Step 2: Rearrange the terms.

We can start by isolating the terms involving $w$ and $x$.

$-7w = -2x - 1 - 49$ $-7w = -2x - 50$

Step 3: Solve for $w$ in terms of $x$.

Now, divide both sides by $-7$: $w = \frac{-2x - 50}{-7}$

Simplifying: $w = \frac{2x + 50}{7}$

Thus, the solution is: $w = \frac{2x + 50}{7}$

Would you like any further explanation or have any questions?

Relative Questions:

1. How do we approach solving for one variable in terms of another?
2. What is the purpose of distributing in algebraic expressions?
3. Why is dividing by a negative number necessary in this step?
4. How does this equation change if $x = 0$?
5. What would happen if we wanted to isolate $x$ instead of $w$?

Tip:

Always ensure you distribute negative signs carefully when solving equations, as they can change the outcome significantly.