https://file.aiquickdraw.com/mathbot/file/1726695798705asiqq87t.jpg

Let's solve the equation:

\[
-9 = \frac{-1}{2} (2 - 8r)
\]

### Step 1: Eliminate the fraction

Multiply both sides of the equation by 2 to get rid of the fraction:

\[
2(-9) = -1(2 - 8r)
\]

\[
-18 = -(2 - 8r)
\]

### Step 2: Simplify the equation

Distribute the negative sign on the right-hand side:

\[
-18 = -2 + 8r
\]

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

Add 2 to both sides:

\[
-18 + 2 = 8r
\]

\[
-16 = 8r
\]

Now, divide both sides by 8:

\[
r = \frac{-16}{8}
\]

\[
r = -2
\]

Thus, the solution is:

\[
r = -2
\]

Would you like further explanation on any step? 

Here are 5 related questions you might want to explore:

1. How do you handle equations with multiple fractions?
2. Can you solve for \( r \) in another linear equation like \( 5r + 4 = 3r - 10 \)?
3. What happens if we deal with decimals instead of fractions?
4. How would the approach differ if the equation had a variable in the denominator?
5. Can you explain the concept of distributing negatives in more detail?

**Tip:** Always start by simplifying the equation, like clearing fractions or parentheses, to make the solving process easier.

Solve the following equation: -9 = (-1/2)(2 - 8r)

Learn how to solve the linear equation -9 = (-1/2)(2 - 8r) using basic algebraic techniques. The solution involves distributing fractions, simplifying terms, and solving for the variable. This problem is ideal for students in Grades 8-10 looking to strengthen their understanding of linear equations.

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