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.

Learn how to solve the linear equation -7(w - 7) = -2x - 1 step by step. This solution uses algebraic concepts like the distributive property and isolating variables. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation