To solve the equation \(-\frac{1}{2} = -\frac{4}{5}w - \frac{5}{3}\) for \(w\), follow these steps:

### Step 1: Eliminate the fractions by finding a common denominator
First, let's eliminate the fractions by multiplying every term by the least common multiple (LCM) of the denominators. The denominators are 2, 5, and 3. The LCM of 2, 5, and 3 is 30.

Multiply every term by 30:
\[
30 \cdot \left(-\frac{1}{2}\right) = 30 \cdot \left(-\frac{4}{5}w\right) - 30 \cdot \left(-\frac{5}{3}\right)
\]

This simplifies to:
\[
-15 = -24w - 50
\]

### Step 2: Isolate the term involving \(w\)
Add 50 to both sides to isolate the term involving \(w\):
\[
-15 + 50 = -24w
\]
\[
35 = -24w
\]

### Step 3: Solve for \(w\)
Divide both sides by \(-24\) to solve for \(w\):
\[
w = \frac{35}{-24} = -\frac{35}{24}
\]

### Final Answer:
\[
w = -\frac{35}{24}
\]

Would you like more details or have any questions?

Here are 5 related questions to further explore the topic:
1. How would you solve this equation if there were multiple \(w\) terms?
2. What are some strategies for solving equations with multiple fractions?
3. How can you check if your solution is correct?
4. What if the equation involved a square root or another nonlinear term?
5. How would this process change if the equation had different signs or coefficients?

**Tip:** When solving equations with fractions, multiplying through by the least common multiple of the denominators can simplify the problem significantly.

Learn how to solve the equation -1/2 = -4/5w - 5/3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations and fractions. Suitable for high school students.

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