91Ó°ÊÓ

Solving equations is the process of finding the value of the variable that makes the equation true. Here, our goal is to determine the value of the variable \(p\). Let's consider the given equation: \-5p = 75\. The main steps in solving an equation involve manipulating the equation using various algebraic techniques to isolate the variable.
In simpler terms, we perform operations like addition, subtraction, multiplication, or division to both sides of the equation until we get the variable alone on one side. For this example, we used division to isolate \(p\):
\(-5p = 75\)
Divide both sides by \(-5\):
\(p = \frac{75}{-5}\)
This leaves us with:
\(p = -15\)
Hence, the solution to the equation \-5p = 75\ is \(p = -15\).

Verification is the process of checking whether our solution to the equation is correct. It's a way to double-check our work.
To verify the solution, we substitute the value of the variable back into the original equation. If both sides of the equation are equal, then our solution is correct. Here, let's substitute \(p = -15\) back into the original equation:
\-5(-15) = 75\
Calculate the left-hand side:
\-5(-15) = 75\
The left-hand side equals the right-hand side, which means our solution \(p = -15\) is indeed correct. Verification helps to prevent mistakes and ensures that the solution we've computed is accurate.

Isolating variables is a key step in solving equations. It involves getting the variable by itself on one side of the equation. This makes it easier to determine its value.
In this particular exercise, we isolate \(p\) by dividing both sides of the equation by \(-5\).
Start with the equation:
\-5p = 75\
To isolate \(p\), divide both sides by \(-5\):
\p = \frac{75}{-5}\
After performing the division, we get:
\p = -15\
This process of isolating the variable allows us to solve for the unknown directly. Always remember to perform the same operation on both sides of the equation to maintain equality.