Question 15

10x is between 4 and 6

The value of 10x lies within the range of 4 and 6, indicating that the coordinate x is between 0.4 and 0.6 on the number line.

A) 1 and 4

This option is incorrect because if 10x were between 1 and 4, it would imply that x is between 0.1 and 0.4. Since we established that x is between 0.4 and 0.6, this range does not hold true.

B) 4 and 6

This option is correct as it suggests that 10x is greater than 4 and less than 6. This aligns perfectly with the derived range for x, which is between 0.4 and 0.6, thus confirming the validity of this choice.

C) 6 and 8

This option is incorrect because if 10x were between 6 and 8, it would mean that x is between 0.6 and 0.8. Since x has been established to lie between 0.4 and 0.6, this option does not apply.

D) 8 and 12

This option is also incorrect because it implies that 10x is greater than 8, suggesting that x would be greater than 0.8. However, as already determined, x is confined to the range of 0.4 to 0.6, making this option invalid.

Conclusion

The correct answer is B, as it accurately reflects the range of 10x based on the coordinate x on the number line. Other options fail because they suggest ranges for 10x that do not align with the established boundaries for x, thereby confirming that B is the only viable choice.