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The image you uploaded contains a mathematical problem with several steps organized in a flowchart format.

### Problem Breakdown:
The equation to solve is:

\[
\frac{2(w - 7)}{5} - 1 = 15
\]

### Steps to Solve:

1. **Isolate the fraction term:**
   Add 1 to both sides to eliminate the -1:

   \[
   \frac{2(w - 7)}{5} = 16
   \]

2. **Clear the denominator by multiplying both sides by 5:**

   \[
   2(w - 7) = 80
   \]

3. **Divide by 2:**

   \[
   w - 7 = 40
   \]

4. **Solve for \(w\):**

   \[
   w = 47
   \]

### Solution Check:
Substitute \(w = 47\) back into the original equation to verify:

\[
\frac{2(47 - 7)}{5} - 1 = 15 
\]

\[
\frac{2 \times 40}{5} - 1 = 15 
\]

\[
\frac{80}{5} - 1 = 15 
\]

\[
16 - 1 = 15 
\]

This confirms that \(w = 47\) is the correct solution.

Would you like any additional details or clarifications?

### Related Questions to Explore:
1. How can you solve similar equations with different operations?
2. What if the equation involves additional variables or coefficients?
3. How do you handle equations with both fractions and decimals?
4. Can we use different methods (like graphing) to solve this equation?
5. How does isolating variables help in solving algebraic equations?

**Tip:** Always check your solution by substituting it back into the original equation to verify its accuracy!

Solve the equation: (2(w - 7))/5 - 1 = 15.

Step-by-step solution for solving the linear equation (2(w - 7))/5 - 1 = 15. This algebra problem demonstrates solving equations with fractions and involves isolating the variable through basic operations. Ideal for students in Grades 7-10.

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