5) \( -4=\frac{r}{20}-5 \)

To solve the equation \( -4 = \frac{r}{20} - 5 \), start by isolating the fraction. Add 5 to both sides: \[ -4 + 5 = \frac{r}{20} \] This simplifies to: \[ 1 = \frac{r}{20} \] Now, multiply both sides by 20 to solve for \( r \): \[ r = 20 \cdot 1 = 20 \] So, the solution is \( r = 20 \). Now, how about a fun fact? The concept of isolating a variable in algebra can be traced back to the ancient Greeks, who were among the first to formalize mathematical thought. They used geometric methods to solve equations, laying the groundwork for future algebraic techniques! Still curious? The real-world application of solving equations like this can be seen in budgeting. For example, if you're trying to figure out how much money you need to save each month to reach a goal by a specific time, you could set up an equation just like the one above!