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When we solve an equation, our primary goal is to find the value of the unknown that makes the equation true. A common method to achieve this is to isolate the variable, which means to get the variable by itself on one side of the equation.

Consider the given example \( -\frac{y}{2} = 5 \). The variable 'y' is not alone; it is being divided by 2, and we also have a negative sign in front. To isolate 'y', we need to undo these operations. Since 'y' is divided by 2, we multiply both sides of the equation by -2 (the inverse of \( -\frac{1}{2} \) is -2). Doing this, we have \( y = -10 \). Now, the variable is isolated, meaning it stands alone on one side of the equation, making it easy for us to understand what the variable represents in terms of value.

It's important to maintain the balance of the equation and perform the same operations on both sides. This ensures that the equality still holds true. Isolating the variable is a fundamental skill that allows us to solve linear equations effectively.

After finding the solution to an equation, it's crucial to ensure that it is indeed a valid answer. This is done through equation verification. Verifying the solution helps you confirm whether you have solved the equation correctly.

In our example, we have determined that the solution for \( y \) is -10. We verify this by substituting \( y \) back into the original equation and checking if both sides are equal. We replace 'y' with -10 and perform the arithmetic to find that \( -\frac{-10}{2} = 5 \), which simplifies to \( 5 = 5 \). This equality confirms the correctness of our solution.

Always remember to check your work by performing this verification step. Doing so not only increases your confidence in the solution but also reinforces your understanding of how the components of an equation work together.

Dealing with negative numbers in algebra can be tricky, but it's pivotal for solving equations correctly. A negative in front of a variable or a number changes the sign of the value that follows.

In the context of the presented equation \( -\frac{y}{2} = 5 \), we encountered a negative number when we isolated 'y' by multiplying both sides by -2. It is crucial to remember that multiplying or dividing by a negative number will flip the sign of the result. For instance, while verifying our solution, we substituted -10 for 'y' and had \( -\frac{-10}{2} \) to evaluate. Remembering that a negative divided by a negative results in a positive, we easily find the correct outcome of 5.

Keep in mind that negative numbers, when combined with other algebraic operations, follow specific rules such as the distributive property and the rules for adding and subtracting integers. These rules must be carefully applied to solve equations accurately.