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When solving algebraic equations, one of the key steps is isolating the variable. This means getting the variable by itself on one side of the equation.

In our example, we start with \(-x = 12\). The \(x\) is currently negative, meaning it has a negative sign in front of it. To isolate \(x\), we need to remove this negative sign. A good way to do this is to multiply both sides of the equation by \(-1\). By applying the same operation to both sides, the equality of the equation is maintained. So, we multiply: \(-1 \times -x = -1 \times 12\).

This simplifies to \(x = -12\), and thus, the variable is isolated. Always remember that whatever operation you perform on one side of the equation, you must perform the same on the other side to keep the equation balanced.

After isolating the variable and finding a potential solution, it is crucial to verify that the solution works in the original equation. This step helps ensure that the solution you found is correct.

Using our solution \(x = -12\), we substitute it back into the original equation \(-x = 12\) to check: \(-(-12) = 12\). When we simplify, we get \(12 = 12\).

Since both sides of the equation are equal, it confirms that \(x = -12\) is indeed the correct solution. This verification step is an excellent habit to develop, as it can help catch mistakes and confirm the accuracy of your solutions.

Multiplying by negative numbers is a crucial concept in algebra that often helps in isolating variables and simplifying equations.

In our example, we had the equation \(-x = 12\). To get rid of the negative sign in front of \(x\), we multiplied both sides of the equation by \(-1\). Mathematically, this looked like \(-1 \times -x = -1 \times 12\).

When you multiply two negative numbers, the result is a positive number. Therefore, \(-1 \times -x\) turned into \(x\). On the right side, \(-1 \times 12\) became \(-12\).

This step allowed us to isolate the variable \(x\) and ultimately find the solution \(x = -12\). Remember, multiplying by negative numbers reverses the sign of the original number. For instance:

• \(-1 \times 5 = -5\)
• \(-1 \times 10 = -10\)
• \(-1 \times -7 = 7\)

Understanding how to correctly handle negative numbers is essential for solving algebraic equations efficiently.