To determine which statement accurately describes the given inequalities, we need to evaluate each inequality one by one.
1. Evaluate the first inequality:
[tex]\[
-\frac{4}{3} > -1.3
\][/tex]
Let's compare the decimal values of both sides:
- [tex]\(\frac{4}{3} \approx 1.3333\)[/tex]
- Thus, [tex]\(-\frac{4}{3} \approx -1.3333\)[/tex]
When comparing [tex]\(-1.3333\)[/tex] and [tex]\(-1.3\)[/tex]:
- [tex]\(-1.3333\)[/tex] is less than [tex]\(-1.3\)[/tex] because a more negative number is smaller.
Therefore:
[tex]\[
-\frac{4}{3} > -1.3 \quad \text{is false}
\][/tex]
2. Evaluate the second inequality:
[tex]\[
\frac{1}{2} < 0.5
\][/tex]
Let's compare both sides directly:
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
When comparing [tex]\(0.5\)[/tex] and [tex]\(0.5\)[/tex]:
- Equal values cannot satisfy a strict inequality.
Therefore:
[tex]\[
\frac{1}{2} < 0.5 \quad \text{is false}
\][/tex]
From our evaluations, we found:
- Inequality (i) is false.
- Inequality (ii) is false.
Hence, the statement that accurately describes the inequalities is:
[tex]\[
\text{(i) is false and (ii) is false.}
\][/tex]
Thus, the correct multiple-choice answer is:
[tex]\[
4 \quad \text{(i) is false and (ii) is false.}
\][/tex]
