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In mathematics, isolating the variable is a crucial step when solving equations. To isolate a variable means to manipulate the equation so that the desired variable stands alone on one side of the equation. For instance, in the equation: \[-p = \frac{6}{7}\], the goal is to solve for 'p'. To do this, we need to eliminate the negative sign that is directly affecting 'p'. This can be achieved by multiplying both sides of the equation by \(-1\). This approach adheres to the fundamental principle of equality, which states whatever you do to one side of the equation, you must also do to the other. This results in: \[p = -\frac{6}{7}\]. Now, 'p' is successfully isolated. This method forms the basis of solving linear equations and is a powerful tool in algebra.

Working with negative numbers can sometimes be tricky, but understanding their operations is essential. When solving equations, you may come across negative numbers that you need to manipulate correctly. In the equation provided: \[-p = \frac{6}{7}\], we needed to "flip" the sign to isolate 'p'. Multiplying by \(-1\) turns \(-p\) into \(p\),and simultaneously negates the fraction, changing \(\frac{6}{7}\) into \(-\frac{6}{7}\). A few key points to remember when dealing with negative numbers:

• Multiplying two negative numbers results in a positive number.
• Multiplying a positive number and a negative number results in a negative number.
• Adding a negative number is equivalent to subtracting its positive value.

Recognizing these rules will make handling negative numbers in equations much smoother.

Verification is a vital part of solving equations. It ensures the solution you've found is indeed correct. After isolating 'p', which gave us:\[p = -\frac{6}{7}\], you should check by substituting \(p\) back into the original equation. The original equation was:\[-p = \frac{6}{7}\]. By substituting \(-\frac{6}{7}\) for \(p\), we have:\[-(-\frac{6}{7}) = \frac{6}{7}\]. The left side becomes \(\frac{6}{7}\), which is equal to the right side. This confirms the solution is correct. Always double-checking your answer like this can help catch errors and solidifies your understanding of the solution process. Remember, any discrepancies during verification usually point to a mistake in calculation, indicating further review is necessary.