What value of $r$ makes $\frac{r}{-11}=-3$ true?
We are given the equation \(\frac{r}{-11} = -3\), where \(r\) is an unknown real number. This is a linear algebraic equation in one variable, and our objective is to find the value of \(r\) that satisfies this equation. We are provided with four possible options: \(-3\), \(33\), \(-33\), and \(3\).
To solve for \(r\), we need to isolate the variable on one side of the equation. We can do this by multiplying both sides of the equation by \(-11\):
\[\frac{r}{-11} \times (-11) = -3 \times (-11)\]
Simplifying the left side, the \(-11\) terms cancel out, leaving:
\[r = -3 \times (-11)\]
Performing the multiplication on the right side:
\[r = 33\]
Thus, the value of \(r\) that makes the equation true is \(33\).
Comparing our result \(r = 33\) with the given choices:
The calculated value matches option b. Therefore, the correct value for \(r\) is \(33\), corresponding to option b.
In real-life scenarios, simple algebraic equations often represent proportional relationships. For instance, if you are sharing a fixed amount of resources among a group and you know the amount per person, you can determine the total amount. If you have a total debt of \(\$33\) that was divided into 11 equal monthly payments of \(\$3\) each (represented as a negative amount due), you could model this as \(\frac{r}{-11} = -3\), where \(r\) represents the total debt amount you needed to pay back. Solving such equations helps in budgeting, financial planning, and resource allocation.