Question

solve for r.
-13 = \frac{r}{9} + 8
r = \square

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( r \), we subtract 8 from both sides of the equation \(-13=\frac{r}{9}+8\). This gives us \(-13 - 8=\frac{r}{9}+8 - 8\). Simplifying the left - hand side: \(-13-8=-21\), and the right - hand side becomes \(\frac{r}{9}\) (since \(8 - 8 = 0\)). So the equation is now \(-21=\frac{r}{9}\).

Step2: Multiply both sides by 9

To solve for \( r \), we multiply both sides of the equation \(-21=\frac{r}{9}\) by 9. Using the property of equality \(a = \frac{b}{c}\Rightarrow b=a\times c\) (where \(a=-21\), \(b = r\), and \(c = 9\)), we get \(r=-21\times9\).

Step3: Calculate the product

Calculating \(-21\times9\), we know that \(21\times9 = 189\), and since one of the factors is negative, the product is negative. So \(r=-189\).

Answer:

\(-189\)