To determine which inequality is true, let’s analyze each one carefully.
1. Inequality: [tex]\( -1.5 > -0.5 \)[/tex]
To compare these numbers, note that on the number line, [tex]\( -1.5 \)[/tex] is to the left of [tex]\( -0.5 \)[/tex], since [tex]\( -1.5 \)[/tex] is more negative. Therefore:
[tex]\[
-1.5 > -0.5 \quad \text{is false}.
\][/tex]
2. Inequality: [tex]\( -\frac{1}{2} > 0 \)[/tex]
Here, we are comparing [tex]\( -0.5 \)[/tex] and 0. Since [tex]\( -0.5 \)[/tex] is a negative number and 0 is neither positive nor negative:
[tex]\[
-0.5 > 0 \quad \text{is false}.
\][/tex]
3. Inequality: [tex]\( -2.5 < -2 \)[/tex]
For this inequality, observe that [tex]\( -2.5 \)[/tex] is further to the left of [tex]\( -2 \)[/tex] on the number line, as it is more negative:
[tex]\[
-2.5 < -2 \quad \text{is true}.
\][/tex]
4. Inequality: [tex]\( -1 \frac{1}{2} > 1.5 \)[/tex]
Convert the mixed number to an improper fraction or decimal to compare:
[tex]\[
-1 \frac{1}{2} = -1.5
\][/tex]
Comparing [tex]\( -1.5 \)[/tex] and 1.5, note that [tex]\( -1.5 \)[/tex] is a negative number and is always less than any positive number:
[tex]\[
-1.5 > 1.5 \quad \text{is false}.
\][/tex]
After this analysis, we conclude that the true inequality is:
[tex]\[
-2.5 < -2
\][/tex]
Therefore, the correct inequality is:
[tex]\[
-2.5 < -2
\][/tex]
This inequality is true.
