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Solving equations is a fundamental concept in algebra that involves finding the value of the variable that makes the equation true. In the given exercise, we are tasked with solving the equation \(-21x = -126\)\. To solve this, we use mathematical operations to isolate the variable and determine its value.

In the context of this problem, we apply the multiplication principle. This means we perform the same operation on both sides of the equation to keep it balanced. By maintaining this balance, we ensure that the equality holds, leading us to the correct solution.

Each step in solving equations should be carefully executed to avoid errors. Practicing such problems helps build a solid understanding of algebraic concepts, making it easier to tackle more complex equations in the future.

Variable isolation is the process of rearranging an equation to get the variable by itself on one side of the equation. This helps us solve for the unknown value. In our example, the variable to isolate is x.

To isolate x in the equation \(-21x = -126\), we need to eliminate the coefficient of x, which is -21. We accomplish this by dividing both sides of the equation by -21:
\(\frac{-21x}{-21} = \frac{-126}{-21}\)
This simplifies to:
\(x = 6\)

By isolating the variable, we transform the equation into a simpler form that directly gives us the value of x. Understanding how to isolate variables is crucial for solving equations efficiently and accurately, allowing us to work through problems methodically.

Equation verification ensures that our solution is correct. After solving for the variable, we substitute the value back into the original equation to see if it holds true. This step is crucial because it confirms the accuracy of our solution.

In the context of the given problem, we found that \(x = 6\). To verify, we substitute this value into the original equation \(-21x = -126\):
\(-21 \times 6 = -126\)

Calculating the left side gives:
\(-126 = -126\)

Since both sides of the equation are equal, our solution is verified as correct. This step provides confirmation and boosts our confidence in our mathematical procedures. Always remember to verify your solution to avoid mistakes and ensure the accuracy of your work.