Question

Solve the proportion. Check for extraneous solutions. $$\frac{r+4}{3}=\frac{r}{5}$$

Short answer

Consequently, the solution to the proportion is \(r = -10\).

Step-by-step solution

Cross Multiply

To solve the proportion, that is \(\frac{r+4}{3}=\frac{r}{5}\), use the cross multiplication method. Multiply \(3*r\) and \(5*(r+4)\), which results in \(3r = 5r + 20\).

Solve the equation

Subtract \(5r\) on both sides of \(3r = 5r + 20\), get \(-2r = 20\). Then, divide both sides by -2 to solve for 'r'. Consequently, \(r = -10\).

Verify the Solution

Replace 'r' by -10 into the original equation: Check if \(\frac{-10+4}{3} = \frac{-10}{5}\). By simplifying both sides, we get \(-2 = -2\), which means that the two sides of the original equation are equal, therefore -10 is not an extraneous solution.