We start by solving the equation:

\[
\frac{x}{-10} + 9 = 1
\]

### Step 1: Subtract 9 from both sides
\[
\frac{x}{-10} = 1 - 9
\]
\[
\frac{x}{-10} = -8
\]

### Step 2: Multiply both sides by -10 to eliminate the denominator
\[
x = -8 \times (-10)
\]
\[
x = 80
\]

So, the solution is:
\[
x = 80
\]

Would you like more details on any step or have any questions?

Here are 5 related questions:
1. What happens if the denominator was positive, say \(\frac{x}{10} + 9 = 1\)?
2. How would you solve \(\frac{x}{-5} + 4 = 0\)?
3. Can you generalize the steps to solve any equation of the form \(\frac{x}{a} + b = c\)?
4. How does the solution change if the fraction's numerator has more terms, like \(\frac{x+2}{-10} + 9 = 1\)?
5. How would you check if the solution to \(\frac{x}{-10} + 9 = 1\) is correct?

**Tip:** When solving linear equations with fractions, it's often easiest to eliminate the denominator early by multiplying both sides of the equation.

Learn how to solve the linear equation \frac{x}{-10} + 9 = 1 with a detailed step-by-step solution. This problem covers algebraic concepts such as fractions, inverse operations, and properties of equality. Suitable for students in Grades 6-8.

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