https://file.aiquickdraw.com/mathbot/file/17277898871639ir1imm3.jpg

The inequality shown in the image is \( \frac{r}{4} < -4 \).

To solve for \( r \), we will first eliminate the denominator by multiplying both sides of the inequality by 4:

\[
\frac{r}{4} \cdot 4 < -4 \cdot 4
\]

This simplifies to:

\[
r < -16
\]

So, the values of \( r \) that satisfy the inequality are all numbers less than \( -16 \).

Looking at the options in the image:
- \( -24 \)
- \( -20 \)
- \( -19 \)
- \( -17 \)

These numbers all satisfy \( r < -16 \).

For the equivalent inequality:
The answer is \( r < -16 \).

Would you like more details or have any other questions?

Here are 5 related questions you can explore:
1. How would the inequality change if the right-hand side was positive?
2. What would happen if the inequality sign was flipped?
3. Can you graph the solution set on a number line?
4. What is the solution if the inequality was \( \frac{r}{4} \leq -4 \)?
5. How would you solve a similar inequality involving fractions with different denominators?

**Tip:** Always remember to flip the inequality sign if you multiply or divide by a negative number while solving inequalities!

Select the values that make the inequality r/4 < -4 true. Then write an equivalent inequality, in terms of r.

Learn how to solve the inequality r/4 < -4 by multiplying both sides by 4 to eliminate the fraction. This example covers essential concepts of algebra and inequalities, suitable for Grades 8-10.

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