Question

Select the three inequalities that are equivalent to r>−11 .(3 points)Responses3r>−333 r is greater than negative 33−3r>33negative 3 r is greater than 333r<−333r<−33−r<11−r<11−3r>33negative 3 r is greater than 33

Answer 1

To determine which inequalities are equivalent to \( r > -11 \), we can manipulate the given options to see if they can be derived from that base inequality.

1. **Multiply by 3**:
- If we multiply \( r > -11 \) by 3, we get:
\[
3r > -33
\]

2. **Multiply by -3**:
- If we multiply \( r > -11 \) by -3, we need to flip the inequality:
\[
-3r < 33 \quad \text{(which is equivalent to \( r < -11 \) when we divide by -3)}
\]

3. **Rearranging**:
- We can also rearrange \( r > -11 \) to get:
\[
-r < 11 \quad \text{(flipping both sides of the inequality)}
\]

### Comparison with Given Responses:
Now let's compare these derived inequalities with the responses:

1. **\( 3r > -33 \)** (Equivalent)
2. **\( -3r < 33 \)** (Equivalent)
3. **\( -r < 11 \)** (Equivalent)

### Summary of the equivalent inequalities:
The equivalent inequalities to \( r > -11 \):
1. \( 3r > -33 \)
2. \( -3r < 33 \)
3. \( -r < 11 \)

Therefore, the correct equivalent inequalities to \( r > -11 \) are:
1. \( 3r > -33 \)
2. \( -3r > 33 \) (which is incorrect, it should be \(-3r < 33\))
3. \( -r < 11 \)

Make sure to double-check the correct format of the inequalities before final selection.