91Ó°ÊÓ

When faced with an equation that needs solving, the goal is to isolate the variable. In this case, the variable is negatively marked, and we'll use the multiplication principle to find its value. The given equation is:
\[ 50 = -x \]
Here, the variable \(x\) is being multiplied by \(-1\). To eliminate this negative sign and isolate \(x\), we need to multiply both sides of the equation by \(-1\). This will balance out the equation and allow us to solve for \(x\).

By multiplying both sides:
\[ 50 \times (-1) = (-x) \times (-1) \]
This simplifies to:
\[ -50 = x \]
Thus, the solution is:
\[ x = -50 \]
It's important to note that performing the same operation on both sides of the equation maintains its balance and integrity.

The multiplication principle is a powerful tool in algebra. It states that if you multiply both sides of an equation by the same non-zero number, the equality is preserved.

Let's see why this is essential:

• It helps remove coefficients or negative signs attached to the variable.
• It keeps the equation balanced, ensuring the left side is always equal to the right side.

In our example, we applied the principle by multiplying both sides by \(-1\):
\[ 50 \times (-1) = (-x) \times (-1) \]
This step was crucial to isolate \(x\) and simplify the equation. By following this method, we maintain a correct and balanced equation, which gives us a valid solution: \( x = -50 \). Remember, every multiplication operation must be done on both sides to keep the equation true.

After solving for the variable, it's crucial to verify that your solution is correct. By substituting the found value back into the original equation, we can check its validity.

In our example, our solution was:
\( x = -50 \)
To check this, we substitute \(x\) back into the original equation:
\[ 50 = -(-50) \]
Simplifying the right side, we get:
\[ 50 = 50 \]
Since both sides of the equation match, our solution is verified as correct. This step ensures that no mistakes were made during the solving process.

Always remember:

• Substituting the solution back into the original equation helps confirm its correctness.
• Consistency between both sides proves the accuracy of your solution.

By following this process, you develop a habit of double-checking your work, leading to fewer errors and greater understanding.