91Ó°ÊÓ

Solving equations is a fundamental concept in algebra. It's about finding the value of a variable that makes the equation true. In our exercise, we need to solve for the variable \(x\) in the equation \(-x = 23\). To solve this, we use strategies like the multiplication principle. Understanding how to manipulate equations by performing the same operation on both sides helps maintain equality.

The multiplication principle is especially useful. It tells us that we can multiply both sides of an equation by the same non-zero number without changing the solution. Here’s how it works:

• First, identify the equation: \(-x = 23\)
• Decide on the operation to isolate \(x\). In this case, we multiply by \(-1\)
• Perform the operation on both sides to keep the equation balanced.

This approach helps us maintain the balance of the equation, ensuring we don’t change the original relationship between \(x\) and the numbers involved.

Isolating variables is a crucial step in solving equations. By isolating, we mean getting the variable alone on one side of the equation. This allows us to directly read off its value. In our equation \(-x = 23\), \(x\) is negative, so we need to eliminate the negative sign.

To do this, we'll multiply both sides by \(-1\):

• This changes \(-x\) to \(x\) because \((-1) \times (-x) = x\)
• Similarly, it changes \(23\) to \(-23\) because \(23 \times (-1) = -23\)

Now, we have \(x = -23\). Notice how we’ve used the multiplication principle to isolate \(x\). By multiplying both sides by \(-1\), we effectively isolate the variable, transforming the original equation into a simple form where \(x\) stands alone.

Checking your solutions is an essential final step. It ensures that the value you've found really satisfies the original equation. For the exercise \(-x = 23\), we found that \(x = -23\). Let’s substitute \(-23\) back into the original equation to verify:

Substitute \(x\) with \(-23\):

\(-(-23) = 23\)

Simplify the left side:

\(23 = 23\)

Since both sides of the equation are equal, \(x = -23\) is indeed the correct solution. This check is necessary to confirm that no mistakes were made during the solving process. Always substitute your solution back into the original equation to see if it holds true. This step strengthens your understanding and ensures accuracy in algebra.