https://file.aiquickdraw.com/mathbot/file/17261186329301835wydy.jpg

The equation provided in the image is:

\[
-\frac{1}{2} + \frac{7}{8}w = -\frac{1}{4}
\]

### Steps to solve for \( w \):

1. First, isolate the term with \( w \). To do this, add \( \frac{1}{2} \) to both sides of the equation:

\[
\frac{7}{8}w = -\frac{1}{4} + \frac{1}{2}
\]

2. Next, simplify the right-hand side. Find a common denominator between \( \frac{1}{4} \) and \( \frac{1}{2} \). The common denominator is 4, so:

\[
\frac{1}{2} = \frac{2}{4}
\]

Thus, the equation becomes:

\[
\frac{7}{8}w = -\frac{1}{4} + \frac{2}{4} = \frac{1}{4}
\]

3. Now, solve for \( w \) by multiplying both sides of the equation by the reciprocal of \( \frac{7}{8} \), which is \( \frac{8}{7} \):

\[
w = \frac{1}{4} \times \frac{8}{7} = \frac{8}{28} = \frac{2}{7}
\]

Thus, the solution is:

\[
w = \frac{2}{7}
\]

Would you like more details on any of these steps?

### Related questions:
1. How do you handle equations with fractions?
2. What is the process for finding a common denominator?
3. Can you explain why multiplying by the reciprocal solves for \( w \)?
4. How can you check if a solution to an equation is correct?
5. How would this equation change if the fraction on the right side was \( \frac{1}{3} \) instead?

### Tip:
Always simplify fractions early in the process to avoid complex calculations later.

Solve for w: -1/2 + (7/8)w = -1/4. Simplify your answer as much as possible.

Learn how to solve the linear equation -1/2 + (7/8)w = -1/4, including steps to find common denominators and simplify fractions. This problem involves key algebraic concepts like isolating variables and solving equations with fractions. Suitable for students in Grades 8-10.

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