To solve the inequality [tex]\(\frac{r}{-3.5} > 2.1\)[/tex] for [tex]\(r\)[/tex], follow these steps:
1. Understanding the Inequality:
[tex]\[
\frac{r}{-3.5} > 2.1
\][/tex]
This tells us that a number divided by [tex]\(-3.5\)[/tex] is greater than [tex]\(2.1\)[/tex].
2. Isolate [tex]\(r\)[/tex]:
To isolate [tex]\(r\)[/tex], we need to multiply both sides of the inequality by [tex]\(-3.5\)[/tex]. However, it is crucial to remember that multiplying or dividing an inequality by a negative number reverses the inequality sign.
So, multiply both sides by [tex]\(-3.5\)[/tex]:
[tex]\[
r < 2.1 \times -3.5
\][/tex]
3. Perform the Multiplication:
Calculate [tex]\(2.1 \times -3.5\)[/tex]:
[tex]\[
2.1 \times -3.5 = -7.35
\][/tex]
4. Write the Solution:
After performing the multiplication and reversing the inequality sign, we get:
[tex]\[
r < -7.35
\][/tex]
5. Find the Correct Multiple Choice Answer:
We need to compare the result with the given options:
- [tex]\(r < -3185\)[/tex]
- [tex]\(r > -31.85\)[/tex]
- [tex]\(r < -26\)[/tex]
- [tex]\(r > 26\)[/tex]
Our solution [tex]\(r < -7.35\)[/tex] matches none of the options exactly. However, it is concerning that there are no valid answers provided based on our calculation. Upon a deeper inspection, it could be a possible mistake in the question's options.
Thus, based on our calculations:
[tex]\[ r < -7.35 \][/tex]
Since this isn't listed among the provided options, we should either reconsider our steps if there was a calculation error or recognize the options themselves might be incorrect.
