Math Skill: Number Line Inequalities

Instructional videos are displayed with permission from Khan Academy.

## Number Line Inequalities

### What is an Inequality?

An inequality is a representation for all the possible values for a variable. It is best understood when compared to an equation with an equal sign. Refer to the chart below:Expression | How You Say It | Meaning |
---|---|---|

x=5 | x equals 5 | x is 5 and nothing else. |

x>6 | x is greater than 6 | x can be any value that is larger than 6, but not equal to 6. For example, x can be 7, 25, 145, 6.001. |

x<-3 | x is less than negative 3 | Valid values include -3.5, -4, -1902, etc., but not -3. |

x≥2 | x is greater than or equal to 2 | Valid values include 2, 2.001, 5, 987324, etc. Note the significance that it can equal 2. |

x≤2 | x is less than or equal to 2 | Valid values include 2,1,0.5,-1523, etc. Note the significance that it can equal 2. |

### Inequalities on a Number Line

Inequalities like "x<5", "x≥3", etc. can be represented on a number line. The standard approach is to draw a circle around the point and then draw a line to the right or to the left, depending on if the value is greater than or less than. If it can also be equal, you fill in the circle. It's easiest to learn if you just follow the examples below.

Number Line | Expression | Explanation |
---|---|---|

x≤6 | Less than: Arrow to the left Equal: Filled in circle | |

x<0 | Less than: Arrow to the left Not Equal: Hollow circle | |

x>-5 | Greater than: Arrow to the right Not Equal: Hollow circle | |

x≥8 | Greater than: Arrow to the right Equal: Filled in circle | |

x<5 or x≥7 | Two separate lines requires use of or. | |

x<-3 or x>-3 Alternate: x≠-3 | Special Case: x is anything but -3 | |

2≤x≤6 Alternate: x≥2 and x≤6 | No outward arrows means we have an and condition. The domain of x is confined between 2 and 6 | |

-4<x≤2 Alternate: x>-4 and x≤2 | -4<x≤2 is preferred, but the alternate is acceptable. | |

2<x<5 Alternate: x>2 and x<5 | 2<x<5 is preferred, but the alternate is acceptable. | |

x=3 | This is not an inequality, but this equation is here to let you know what it looks like. |