Which statement accurately describes the inequalities below?

(i) [tex]-\frac{4}{3}\ \textgreater \ -1.3[/tex]
(ii) [tex]\frac{1}{2}\ \textless \ 0.5[/tex]

A. (i) is false and (ii) is true.
B. (i) is true and (ii) is true.
C. (i) is true and (ii) is false.
D. (i) is false and (ii) is false.



Answer :

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]