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In algebra, isolating the variable means getting the variable alone on one side of the equation. This usually involves performing inverse operations. For example, if the variable is being subtracted, you add the same value to both sides. In the given problem, we start with the equation \-x = -\frac{3}{4}\. Here, \(-x\) represents the variable term with a negative sign. To isolate \(x\), we need to get rid of the negative sign by multiplying both sides of the equation by \(-1\):\ -x \cdot (-1) = -\frac{3}{4} \cdot (-1). After performing this step, we simplify to obtain \(x = \frac{3}{4}\). This gives us the isolated variable \(x\) on one side. Remember, the key is to perform the same operation on both sides of the equation.
Performing inverse operations and maintaining the balance of the equation are crucial steps in isolating variables. This way, you can solve for the variable effectively.

Negative numbers can sometimes make equations look more complicated than they are. In our exercise, both sides of the equation had negative signs: \(-x = -\frac{3}{4}\). Understanding how to handle them is important. Here are some key points:
- Multiplying or dividing both sides of an equation by a negative number will change the signs.
- Two negative signs cancel out, resulting in a positive number.
For instance, when we multiplied both sides by \(-1\), the equation \(-x = -\frac{3}{4}\) became \(x = \frac{3}{4}\). This makes it easier to solve. It's helpful to remember these rules when dealing with negative numbers, as they allow you to simplify and solve equations more effectively. Practice makes perfect, so encountering a variety of problems will strengthen your understanding.

Once you've isolated the variable and found a solution, it's vital to verify that your solution is correct. This is the final step to ensure accuracy. In our solved equation, we found \(x = \frac{3}{4}\). To verify:
- Substitute \(x = \frac{3}{4}\) back into the original equation: \-\left( \frac{3}{4} \right) = -\frac{3}{4}.
- Simplify the left side to ensure it equals the right side: \-\frac{3}{4} = -\frac{3}{4}.
Both sides are equal, proving that \(x = \frac{3}{4}\) is indeed the correct solution. Always double-check your solution by substituting it back into the original equation. This confirms that the operations performed were correct and that no mistakes were made. It's a crucial habit to develop for all algebra problems.