Question

Which inequality is true?

A number line going from negative 3 to positive 3 in increments of 1.
One-fourth less-than negative 1 and StartFraction 2 Over 4 EndFraction
Negative 2 and three-fourths less-than negative 1 and one-half
Negative 2 and one-fourth greater-than negative 1 and one-fourth
Negative three-fourths greater-than 1 and three-fourths

Answer 1

To determine which inequality is true, let's evaluate each one separately.

1. **One-fourth less than negative 1 and \( \frac{2}{4} \)**:
- One-fourth less than -1 is \( -1 - \frac{1}{4} = -1.25 \) (or -5/4).
- \( \frac{2}{4} = \frac{1}{2} = 0.5 \).
- Inequality: \( -1.25 < 0.5 \) (True)

2. **Negative 2 and three-fourths less than negative 1 and one-half**:
- Negative 2 and three-fourths is \( -2.75 \) (or -11/4).
- Negative 1 and one-half is \( -1.5 \) (or -3/2).
- Inequality: \( -2.75 < -1.5 \) (True)

3. **Negative 2 and one-fourth greater than negative 1 and one-fourth**:
- Negative 2 and one-fourth is \( -2.25 \) (or -9/4).
- Negative 1 and one-fourth is \( -1.25 \) (or -5/4).
- Inequality: \( -2.25 > -1.25 \) (False)

4. **Negative three-fourths greater than 1 and three-fourths**:
- Negative three-fourths is \( -0.75 \) (or -3/4).
- One and three-fourths is \( 1.75 \).
- Inequality: \( -0.75 > 1.75 \) (False)

Now, summing up:
- The first two inequalities are true:
- \( -1.25 < 0.5 \) (True)
- \( -2.75 < -1.5 \) (True)

- The last two inequalities are false.

Both the first and second statements are true. If asked to select only one, the first statement is generally stated without ambiguity in its phrasing.