Solve for $p$.
$-4 p = -16$
$-4 p = -16$
Solve for $p$.
$-4 p = -16$
The problem asks us to solve for the variable \(p\) in the linear equation \(-4p = -16\). A linear equation of the form \(ap = b\) can be solved by isolating the variable \(p\). In this case, \(a = -4\) and \(b = -16\). To isolate \(p\), we divide both sides of the equation by the coefficient of \(p\), which is \(-4\).
To solve for \(p\), we divide both sides by \(-4\):
\[\frac{-4p}{-4} = \frac{-16}{-4}\]
Simplifying the left side, \(\frac{-4p}{-4}\) becomes \(p\). On the right side, \(\frac{-16}{-4}\) equals \(4\) because a negative number divided by a negative number is a positive number. Therefore, we find that \(p = 4\).
Linear equations like this are found everywhere in daily budgeting. For instance, if you bought 4 identical notebooks for a total of \(\$16\) and want to find the price of one notebook, you can model this as \(4p = 16\), where \(p\) is the price per notebook. Solving this equation helps you quickly calculate unit prices, allowing you to compare deals and manage your money effectively.