https://file.aiquickdraw.com/mathbot/file/17261045217078ogq7d9y.jpg

The equation from the image is:

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

Let's solve for \( w \):

### Step 1: Move the constant term to the other side

Add \(\frac{1}{2}\) to both sides to isolate the \(w\)-term:
\[
\frac{1}{5}w = -\frac{1}{3} + \frac{1}{2}
\]

### Step 2: Find a common denominator and simplify

The least common denominator between 3 and 2 is 6:
\[
-\frac{1}{3} + \frac{1}{2} = -\frac{2}{6} + \frac{3}{6} = \frac{1}{6}
\]

So the equation becomes:
\[
\frac{1}{5}w = \frac{1}{6}
\]

### Step 3: Solve for \(w\)

Multiply both sides by 5 to isolate \(w\):
\[
w = 5 \times \frac{1}{6} = \frac{5}{6}
\]

Thus, the solution is:
\[
w = \frac{5}{6}
\]

Would you like a further breakdown of any step? Here are some related problems to deepen your understanding:

1. Solve \(\frac{2}{3}w - \frac{1}{4} = \frac{5}{6}\) for \(w\).
2. Solve \(2w - \frac{3}{5} = \frac{4}{7} - w\) for \(w\).
3. Simplify \(\frac{5}{8} - \frac{2}{3}\) and express the result as a fraction.
4. Solve \(\frac{2}{w} + 3 = 5\) for \(w\).
5. Solve \( \frac{w}{2} + \frac{w}{3} = \frac{5}{6} \).

**Tip:** Always look for common denominators when adding or subtracting fractions to make simplification easier.

Learn how to solve the linear equation -1/2 + 1/5w = -1/3. This solution provides a step-by-step guide to solving for w, involving fraction addition, simplification, and isolating the variable. Ideal for students in Grades 6-8.

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