Comparing Integers on a Horizontal Number Line
Comparing Integers on a Horizontal Number Line is a Grade 6 math skill from Big Ideas Math Advanced 1, Chapter 6 (Integers and the Coordinate Plane) that teaches students to use inequality symbols (<, <=, >, >=) to compare integers. On a number line, a < b means a is to the left of b, and a > b means a is to the right. Unlike equations, inequalities describe ranges of possible integer values.
Key Concepts
For any two integers $a$ and $b$: $a < b$ means "$a$ is less than $b$." $a \leq b$ means "$a$ is less than or equal to $b$." $a b$ means "$a$ is greater than $b$." $a \geq b$ means "$a$ is greater than or equal to $b$.".
On a number line, $a < b$ means that $a$ lies to the left of $b$, and $a b$ means that $a$ lies to the right of $b$.
Common Questions
How do you compare integers using a number line?
On a horizontal number line, numbers increase from left to right. If a is to the left of b, then a < b. If a is to the right of b, then a > b. For example, -3 is to the left of 2, so -3 < 2.
What do inequality symbols mean when comparing integers?
< means less than (to the left on a number line). > means greater than (to the right). <= means less than or equal to. >= means greater than or equal to. For example, x > -2 means x can be -1, 0, 1, 2, etc.
What chapter covers comparing integers in Big Ideas Math Advanced 1?
Comparing integers on a horizontal number line is covered in Chapter 6 of Big Ideas Math Advanced 1, titled Integers and the Coordinate Plane, for Grade 6.
How is an inequality different from an equation when comparing integers?
An equation has one specific solution. An inequality describes a range of integer values. For example, x >= -5 includes -5, -4, -3, -2, -1, 0, 1, 2, ... — infinitely many solutions.
What is an example of comparing integers with inequalities?
The statement x > -2 means x can be any integer to the right of -2: -1, 0, 1, 2, 5, etc. The statement -5 <= y means y can be -5 or any integer to its right on the number line.