91Ó°ÊÓ

Solving equations is a fundamental aspect of algebra where we find the value of an unknown variable. In this context, we're dealing with an equation \( \frac{x}{-7} = 12 \)\, where the goal is to determine what value \( x \) must be so that when divided by \(-7\) it equals \(12\). The process of solving equations generally involves performing operations that will help simplify the equation. We employ techniques such as addition, subtraction, multiplication, and division, to "undo" the operations affecting the variable. The main goal here is to rearrange the equation in such a way that the variable is isolated; essentially, solving the puzzle one piece at a time. This methodical approach ensures that we correctly address each component of the equation, ultimately leading us to the solution.

Isolating the variable is like unveiling the secret hidden within the equation. In the equation \( \frac{x}{-7} = 12 \), \( x \) is shrouded by a division with \(-7\). Our task is to remove this obstruction to reveal \( x \). To do this, we need to perform the opposite operation of what's being done to \( x \). Currently, \( x \) is being divided, so we'll multiply. Multiply both sides of the equation by \(-7\), the very same number which creates the division barrier. This gives us the simple equation: \( x = 12 \times (-7) \). This multiplication cancels out the division on the left side, leaving us with \( x = -84 \). We've successfully unveiled \( x \) and completed this step of isolating the variable and discovering its true value.

Verifying the solution is an important step to ensure accuracy in math problems. After finding the solution, it's crucial to check it. For our equation, we calculated \( x = -84 \). Let’s substitute \(-84\) back into the original equation to see if it holds true: \( \frac{-84}{-7} = 12 \). When we perform the division of \(-84\) by \(-7\), we indeed get \(12\). This final step confirms that our solution is correct. Verification can act as a safeguard against mistakes and assures us that our mathematical journey was spot on. So, always remember, verifying isn't just an optional step; it’s a essential key to validating your work.