https://file.aiquickdraw.com/mathbot/file/1727114872069bwefjl9x.jpg

The equation from the image is:

\[
-31 = -39 - \frac{y}{8}
\]

Let's solve for \( y \).

### Step 1: Isolate the term with \( y \)
We want to move the constant term on the right-hand side, \(-39\), to the left-hand side. Add 39 to both sides:

\[
-31 + 39 = - \frac{y}{8}
\]

\[
8 = - \frac{y}{8}
\]

### Step 2: Solve for \( y \)
To get rid of the fraction, multiply both sides by \(-8\):

\[
8 \times (-8) = y
\]

\[
y = -64
\]

Thus, the solution is \( y = -64 \).

Would you like further details on any step?

Here are some related questions for you:
1. How would the process change if the fraction had a different denominator?
2. What if the equation was \( -31 = -39 + \frac{y}{8} \)?
3. How do you handle two-step equations with variables on both sides?
4. How can you check if your solution is correct?
5. What if \( y \) were in the numerator instead of a fraction?

**Tip:** Always check your solution by substituting it back into the original equation.

Step-by-step solution to the algebraic equation -31 = -39 - y/8, demonstrating how to isolate variables and perform operations with fractions. Ideal for students in Grades 7-9 looking to master basic algebraic operations.

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