Question

Which statements of inequality are supported by the number line? 1) -1 < -8 2) 0 < -8 < 2 < 8 3) 8 > -8 4) -8 < -1 < 2 5) 2 < 8

Answer 1

Upon examining each inequality against the logic of a number line, we find that statements 3) 8 > -8, 4) -8 < -1 < 2, and 5) 2 < 8 are true. The other statements are incorrect based on the positioning of numbers on a standard number line.

Step-by-step explanation:

To determine which statements of inequality are supported by the number line, we need to evaluate each statement individually:

1. -1 < -8 is not true because on a number line, -1 is to the right of -8, meaning -1 is greater than -8.
2. 0 < -8 < 2 < 8 is not true because 0 is to the right of -8 on the number line, which means 0 is greater than -8, not less.
3. 8 > -8 is true because 8 is to the right of -8 on the number line, indicating that it is greater.
4. -8 < -1 < 2 is true since -8 is to the left of -1, and -1 is to the left of 2 on the number line, demonstrating that -8 is less than -1, and -1 is less than 2, respectively.
5. 2 < 8 is also true as 2 is to the left of 8 on the number line indicating that 2 is less than 8.

From the above analysis, the correct statements that are supported by the number line are option 3), 4), and 5).