We are given the equation:

\[
\frac{-2}{3w} - \frac{1}{2} = \frac{-4}{5}
\]

Let's solve for \( w \).

### Step 1: Isolate the term with \( w \)
Add \( \frac{1}{2} \) to both sides:

\[
\frac{-2}{3w} = \frac{-4}{5} + \frac{1}{2}
\]

### Step 2: Find a common denominator to add the fractions
The common denominator between 5 and 2 is 10. Rewrite the fractions:

\[
\frac{-4}{5} = \frac{-8}{10}, \quad \frac{1}{2} = \frac{5}{10}
\]

Now, add the fractions:

\[
\frac{-8}{10} + \frac{5}{10} = \frac{-3}{10}
\]

So, we have:

\[
\frac{-2}{3w} = \frac{-3}{10}
\]

### Step 3: Solve for \( w \)
Cross-multiply to solve for \( w \):

\[
-2 \times 10 = -3 \times 3w
\]

This simplifies to:

\[
-20 = -9w
\]

### Step 4: Isolate \( w \)
Divide both sides by -9:

\[
w = \frac{-20}{-9} = \frac{20}{9}
\]

Thus, the solution is:

\[
w = \frac{20}{9}
\]

Would you like more details on any step?

Here are some related questions to try:
1. Solve \( \frac{3}{4w} - \frac{1}{2} = \frac{5}{6} \).
2. Simplify and solve \( \frac{-5}{2w} + \frac{2}{3} = \frac{-7}{4} \).
3. Solve \( 2 - \frac{3}{w} = \frac{5}{6} \).
4. Solve \( \frac{-3}{w + 1} - \frac{1}{3} = 2 \).
5. Find \( w \) in \( \frac{-1}{2w} + \frac{3}{4} = \frac{-5}{6} \).

**Tip:** When solving equations with fractions, finding a common denominator is a key step to simplify the process.

Learn how to solve the linear equation -2/3w - 1/2 = -4/5 by isolating the variable and using cross-multiplication. This problem covers algebraic concepts such as fraction addition and finding common denominators. Suitable for students in Grades 8-10.

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