Compound inequalities are groups of two or more inequalities, called conjunctions if they are connected by the word "and" or disjunctions if they are joined by "or." Conjunctions need both inequalities to be true: For example, 4 satisfies both x>3 and x<5. Disjunctions need just one component to be true: For instance, in x>10 or x<8, 2 can be an option. These terms seem to belong to advanced math textbooks, but actually, compound inequalities have many applications in everyday life.

A tier system is a way of organizing data into distinct categories, called "tiers." Data are placed in each category based on certain criteria, which, for example, can be students' marks, cars' top speed or people's income. The tier ranking system is based on conjunctions: Each tier includes entries better than those of the lower tier, but at the same time worse than entries of the tier above. The result is a chain of inequalities, visualized as Tier 1 > Tier 2 > Tier 3 and so forth.

Compound inequalities allow you to describe the extent of regions, layers or stage. For example, the second layer of the Earth's atmosphere is the stratosphere, which is at least 9 miles and at the most 31 miles over the Earth's surface. If "x" is stratosphere, you can write down this compound inequality as 9<x<31. Similarly, the U.S. National Library of Medicine defines adolescents as those older than 13 years and younger than 19, with the compound inequality in this case being 13<x<19.

Disjunctions are used in real life to describe extreme values on either side of a theoretical axis. An example of such axis can be that of age. To describe the years a person does not work, you must go below 18 and over 65, for example. Therefore, a person who does not work can be x<18 or x>65. Similarly, extreme weather conditions occur when the temperature is above 105 or below 35 degrees Fahrenheit, which you write as x<35 or x>105.

Approximations can take the form of a conjunction, if it's beyond doubt that the exact number cannot be lower or higher than certain values. For example, you may know the exact salary of your friend, but you are sure it's not more than $1,500 and not less than $1,000. Therefore, her salary is $1,000<x<$1,500. Likewise, when you try to determine the age of a man, you may say he is more than 30, but not more than 35, which you can express as 30<x<35.