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When faced with a linear equation, like \(-15x = -60\), the goal is to find the value of the variable that makes the equation true. Solving equations involves performing operations that simplify the equation while maintaining balance.
It's crucial to treat both sides of the equation equally when you manipulate it. For instance, if you divide one side by a number, you must do the same to the other side. This way, the equation remains balanced and correct.
The process can involve several steps, such as:

• Adding, subtracting, multiplying, or dividing both sides by the same number.
• Consolidating like terms.
• Rechecking the logical flow of your operations.

The end goal is to leave the variable by itself on one side of the equation in a simplified form.

To solve \(-15x = -60\), we need to isolate the variable \(x\). Isolation of variables means making the variable stand alone on one side of the equation. This process typically involves the opposite operation of what is being applied to the variable.

In our example, \(-15x = -60\), the variable \(x\) is being multiplied by \(-15\). We need to undo this multiplication to get \(x\) by itself. We do this by dividing both sides of the equation by \(-15\). This step gives us \(x = \frac{-60}{-15}\).

Once we've isolated \(x\), we then simplify further. In this case, both \(-60\) and \(-15\) are divisible by \(-15\), leading to the simplified solution \(x = 4\). Keeping track of these steps ensures precise handling of the equation and an accurate solution.

After finding a solution, verifying it is crucial. This step ensures that the operations performed were correct, yielding a true statement.
To check your solution, substitute the found value back into the original equation. In our case, substituting \(x = 4\) back into the equation \(-15x = -60\) results in \(-15(4) = -60\).

• Start by plugging in your value: \(-15(4)\).
• Calculate the product: \(-60\).
• Compare with the original right side of the equation \(-60\).

If the left side equals the right side upon substitution, the solution is correct. This step not only confirms the accuracy of your solution but also reinforces understanding of the equation and operation relationships.