Question

Select all of the inequalities that are true.
5x3/4 <5
5 x 4/3 > 5
5x1 1/3 > 5
5 x 1/3 <5

Answer 1

Are you sure

Answer 2

Let's evaluate each inequality one by one.

1. **\( 5 \times \frac{3}{4} < 5 \)**:
\[
5 \times \frac{3}{4} = \frac{15}{4} = 3.75
\]
Since \( 3.75 < 5 \), this inequality is true.

2. **\( 5 \times \frac{4}{3} > 5 \)**:
\[
5 \times \frac{4}{3} = \frac{20}{3} \approx 6.67
\]
Since \( 6.67 > 5 \), this inequality is true.

3. **\( 5 \times 1 \frac{1}{3} > 5 \)**:
Convert \( 1 \frac{1}{3} \) to an improper fraction:
\[
1 \frac{1}{3} = \frac{4}{3}
\]
Thus,
\[
5 \times \frac{4}{3} = \frac{20}{3} \approx 6.67
\]
Since \( 6.67 > 5 \), this inequality is true.

4. **\( 5 \times \frac{1}{3} < 5 \)**:
\[
5 \times \frac{1}{3} = \frac{5}{3} \approx 1.67
\]
Since \( 1.67 < 5 \), this inequality is true.

All four inequalities are true:

1. \( 5 \times \frac{3}{4} < 5 \) (True)
2. \( 5 \times \frac{4}{3} > 5 \) (True)
3. \( 5 \times 1 \frac{1}{3} > 5 \) (True)
4. \( 5 \times \frac{1}{3} < 5 \) (True)

Therefore, all of the inequalities selected are true.

Answer 3

Let's go through the inequalities again step by step to ensure accuracy.

1. **\( 5 \times \frac{3}{4} < 5 \)**:
\[
5 \times \frac{3}{4} = \frac{15}{4} = 3.75
\]
Thus, \( 3.75 < 5 \) is **true**.

2. **\( 5 \times \frac{4}{3} > 5 \)**:
\[
5 \times \frac{4}{3} = \frac{20}{3} \approx 6.67
\]
Therefore, \( 6.67 > 5 \) is **true**.

3. **\( 5 \times 1 \frac{1}{3} > 5 \)**:
\( 1 \frac{1}{3} \) converts to:
\[
1 \frac{1}{3} = \frac{4}{3}
\]
Then:
\[
5 \times \frac{4}{3} = \frac{20}{3} \approx 6.67
\]
So, \( 6.67 > 5 \) is **true**.

4. **\( 5 \times \frac{1}{3} < 5 \)**:
\[
5 \times \frac{1}{3} = \frac{5}{3} \approx 1.67
\]
Hence, \( 1.67 < 5 \) is **true**.

After double-checking all calculations, the findings remain the same.

**Final Conclusion**: All four inequalities are indeed true:
1. \( 5 \times \frac{3}{4} < 5 \): True
2. \( 5 \times \frac{4}{3} > 5 \): True
3. \( 5 \times 1 \frac{1}{3} > 5 \): True
4. \( 5 \times \frac{1}{3} < 5 \): True

If there is a specific concern or doubt about one of the inequalities, please let me know so I can address it directly!