Let's solve the equation step by step:

Given equation:
\[
5(1 - 2w) + 8w = 15
\]

### Step 1: Distribute the 5 on the left-hand side
\[
5 \times 1 - 5 \times 2w + 8w = 15
\]
\[
5 - 10w + 8w = 15
\]

### Step 2: Combine like terms
\[
5 - 2w = 15
\]

### Step 3: Isolate the variable term
Subtract 5 from both sides:
\[
-2w = 15 - 5
\]
\[
-2w = 10
\]

### Step 4: Solve for \( w \)
Divide both sides by -2:
\[
w = \frac{10}{-2}
\]
\[
w = -5
\]

### Final Answer:
\[
w = -5
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve an equation with multiple variables?
2. What happens if you add variables on both sides of an equation?
3. How do you handle distribution in algebraic expressions?
4. What does it mean when a variable is negative?
5. How do you check if a solution to an equation is correct?

**Tip:** Always combine like terms first to simplify the equation before solving for the variable.

Explore how to solve the linear equation 5(1-2w) + 8w = 15 step by step. This problem includes key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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