To solve the inequality [tex]\(\frac{r}{-2.5} \leq 8.7\)[/tex] for [tex]\(r\)[/tex], follow these steps:
1. Recognize that you need to isolate the variable [tex]\(r\)[/tex]. The current form of the inequality involves [tex]\(r\)[/tex] being divided by [tex]\(-2.5\)[/tex]. To isolate [tex]\(r\)[/tex], you need to eliminate the division by [tex]\(-2.5\)[/tex].
2. To eliminate the division, multiply both sides of the inequality by [tex]\(-2.5\)[/tex]. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality sign:
[tex]\[
\left(\frac{r}{-2.5}\right) \cdot (-2.5) \geq 8.7 \cdot (-2.5)
\][/tex]
3. Simplify both sides:
[tex]\[
r \geq 8.7 \cdot (-2.5)
\][/tex]
4. Calculate the product on the right side:
[tex]\[
8.7 \cdot (-2.5) = -21.75
\][/tex]
5. Rewrite the inequality with the calculated value:
[tex]\[
r \geq -21.75
\][/tex]
Thus, the solution to the inequality [tex]\(\frac{r}{-2.5} \leq 8.7\)[/tex] is [tex]\(r \geq -21.75\)[/tex].
The correct answer is [tex]\(r \geq -21.75\)[/tex].
