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.