91Ó°ÊÓ

Let's start solving the equation by isolating the variable. In our equation \( -9x = 36 \), the term with our variable is \( -9x \). To isolate \( x \), we need to get rid of the \( -9 \) attached to it.

We can do this by dividing both sides of the equation by \( -9 \). This is important because it helps us to manipulate the equation without changing its meaning. Dividing both sides by the same non-zero number keeps the equation balanced, just like a balanced scale.

After performing the division, we get the simplified form of the equation: \[ x = \frac{36}{-9} \]

This gives us the first step towards finding our solution. Once we've isolated \( x \), it becomes much simpler to work with.

Now that we have isolated our variable, we need to simplify the equation. Simplifying equations involves performing basic arithmetic operations to reduce the equation to its simplest form.

From our isolation step, we have: \[ x = \frac{36}{-9} \]

Next, we divide 36 by \( -9 \), which is a straightforward division. The result is \[ x = -4 \]

Simplifying is crucial as it transforms complex expressions into simpler ones, making them easier to interpret and solve. Always perform these operations carefully and double-check your results.

After finding a potential solution, we should verify if it actually solves the original equation. Verification ensures that no mistakes were made during solving.

For our solved equation, we found \( x = -4 \). To verify, we substitute \( x \) back into the original equation \( -9x = 36 \):

Replacing \( x \) with \( -4 \) gives \[ -9(-4) = 36 \]

Calculating the left-hand side we get \[ 36 = 36 \]

Since both sides of the equation are equal, our solution is verified correct.

Verification should be a final step in any problem-solving process to ensure accuracy and correctness of the solution.