91Ó°ÊÓ

When solving linear equations, the primary goal is to find the value of the variable. This often means you'll need to isolate the variable on one side of the equation.
In our example, the equation is \(-6x = -72\). We need to isolate \(x\). This means we should get \(x\) by itself, without any other numbers or variables attached.
To isolate \(x\) in \(-6x = -72\), we can use the division method. Before jumping into division, make sure to carefully interpret the equation and decide which operation will help you isolate the variable. Here, since \(x\) is multiplied by \(-6\), dividing both sides by \(-6\) will achieve this isolation.
This step is crucial in solving linear equations and forms the foundation for finding the correct solution.

Performing division in equations requires you to divide each term in the equation by the same number. It's essential to remember to apply the division evenly across the entire equation to maintain balance.
In our example, the equation \(-6x = -72\) requires dividing both sides by \(-6\) to isolate \(x\). Hence, we do:
\(-6x \/ -6 = -72 \/ -6\)
When you divide \(-72\) by \(-6\), you get \(+12\). Therefore, \(x\) equals 12.
Remember, maintaining equality on both sides is critical. Incorrect division can lead to the wrong solution, so ensure you divide each term consistently across the equation.

After solving for the variable, it's important to verify that your solution is correct. This is done by substituting the value of the variable back into the original equation.
For our example, once we found \(x = 12\), we substitute this back into the equation \(-6x = -72\). This gives us:
\(-6 \cdot 12 = -72\)
Since the left-hand side of the equation equals the right-hand side, our solution is confirmed to be correct. This step helps to ensure that no errors were made during the isolation and division steps.
Always check your solution to avoid mistakes and to verify the accuracy of your work.