Option C: Three-fourths greater-than two-thirds
Solution:
Option A: A number line going from negative 1 to 1.
Explanation: A number line is used to define a point in a given interval. And hence, a number line does not goes from negative 1 to 1.
Thus, this statement is false.
Option B: One-half less-than one-third
Explanation: The statement can be written as
![\begin{array}{c}{\frac{1}{5}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7D%7B%5Cfrac%7B1%7D%7B5%7D%3C%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%7B0.5%3C0.33%7D%5Cend%7Barray%7D)
which is not possible.
Hence, this inequality is false.
Option C: Three-fourths greater-than two-thirds
Explanation: The statement can be written as
![\begin{array}{c}{\frac{3}{4}>\frac{2}{3}} \\{0.75>0.667}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7D%7B%5Cfrac%7B3%7D%7B4%7D%3E%5Cfrac%7B2%7D%7B3%7D%7D%20%5C%5C%7B0.75%3E0.667%7D%5Cend%7Barray%7D)
which is true.
Hence, this inequality is true.
Option D: Negative one-fourth less-than negative two-thirds
Explanation: The statement can be written as
![\begin{aligned}-\frac{1}{4} &](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-%5Cfrac%7B1%7D%7B4%7D%20%26%3C-%5Cfrac%7B2%7D%7B3%7D%20%5C%5C-0.25%20%26%3C-0.667%5Cend%7Baligned%7D)
This is not possible.
Hence, this inequality is false.
Option E: Negative 1 greater-than three-fourths
Explanation: The statement can be written as
![\begin{array}{l}{-1>\frac{3}{4}} \\{-1>0.75}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B-1%3E%5Cfrac%7B3%7D%7B4%7D%7D%20%5C%5C%7B-1%3E0.75%7D%5Cend%7Barray%7D)
This is not possible.
Hence, this inequality is false.