Intervals and Inequalities

​Inequalities & Interval Notation

​Graphing Inequalities and rewriting inequalities in interval notation.

​Inequality:

a statement that two quantities are not

equal; we use the symbols >, <, ≥, ≤

​

​

​

Number line for graphing inequalities:

• we shade the numbers that the variable could be;

• closed dots mean included (≥, ≤)

• open dots mean not included (>, <)

​

Interval Notation:

a method to represent an interval on a number line.

​Verbal Description	Number LIne​	Inequality​	Interval​
​ ​x is greater than 4	​	​ x > 4	​ (4, ∞)

​Key Words:

greater

more

larger

above​

​

​Greater than

​>

​Verbal Description	Number LIne​	Inequality​	Interval​
​ ​x is less than 4	​	​ x < 4	​ (-∞, 4)

​Key Words:

less

smaller

below​

​

​Less than

​<

​Verbal Description	Number LIne​	Inequality​	Interval​
​ ​x is greater than or equal to 4	​	​ x ≥ 4	​ [4, ∞)

​Key Words:

minimum

at least

no less than

no smaller than​

​

​Greater than or equal to

​≥

​Verbal Description	Number LIne​	Inequality​	Interval​
​ ​x is less than or equal to 4	​	​ x ≤ 4	​ (-∞, 4]

​Key Words:

maximum

at most

no greater than

no more than

no bigger than​

​

​Less than or equal to

​≤

​Verbal Description	Number LIne​	Inequality​	Interval​
​ ​2 is less than x, which is less than or equal to 6	​	​ 2 < x ≤ 6 (inequality signs will always point the same direction)	​ (2, 6]

​Key Words:

between

within

intersection​

​

​AND

​Verbal Description	Number LIne​	Inequality​	Interval​
​ ​x is less than 2, or x is greater than or equal to 6	​	​ x < 2 OR x ≥ 6	​ (-∞, 2) ∪ [6, ∞)

​Key Words:

outside

union​

​

​OR