To determine which inequality is true, let's analyze each one separately.
### Inequality 1
[tex]\[ -1.5 > -0.5 \][/tex]
To compare these numbers on the number line:
- -1.5 is to the left of -0.5 because it is more negative.
- Therefore, -1.5 is less than -0.5, not greater.
So, [tex]\(-1.5 > -0.5\)[/tex] is false.
### Inequality 2
[tex]\[ -\frac{1}{2} > 0 \][/tex]
To compare these numbers:
- -[tex]\(\frac{1}{2}\)[/tex] (which is -0.5) is a negative number.
- 0 is a neutral number, and it is greater than any negative number.
So, [tex]\(-\frac{1}{2} > 0\)[/tex] is false.
### Inequality 3
[tex]\[ -2.5 < -2 \][/tex]
To compare these numbers on the number line:
- -2.5 is to the left of -2 because it is more negative.
- Therefore, -2.5 is less than -2.
So, [tex]\(-2.5 < -2\)[/tex] is true.
### Inequality 4
[tex]\[ -1\frac{1}{2} > 1.5 \][/tex]
To compare these numbers:
- -1[tex]\(\frac{1}{2}\)[/tex] (which is -1.5) is a negative number.
- 1.5 is a positive number, and any positive number is greater than any negative number.
So, [tex]\(-1\frac{1}{2} > 1.5\)[/tex] is false.
### Conclusion
After analyzing each inequality, we find that:
- [tex]\(-1.5 > -0.5\)[/tex] is false.
- [tex]\(-\frac{1}{2} > 0\)[/tex] is false.
- [tex]\(-2.5 < -2\)[/tex] is true.
- [tex]\(-1\frac{1}{2} > 1.5\)[/tex] is false.
Thus, the true inequality is:
[tex]\[ -2.5 < -2 \][/tex]
This corresponds to the third inequality on the list. Therefore, the index of the true inequality is [tex]\(3\)[/tex].
