Math Skill: Number Line Inequalities
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Number Line Inequalities

## 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:
ExpressionHow You Say ItMeaning
x=5x equals 5x is 5 and nothing else.
x>6x is greater than 6x 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<-3x is less than negative 3Valid values include -3.5, -4, -1902, etc., but not -3.
x≥2x is greater than or equal to 2Valid values include 2, 2.001, 5, 987324, etc. Note the significance that it can equal 2.
x≤2x is less than or equal to 2Valid 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 LineExpressionExplanation
x≤6Less than: Arrow to the left
Equal: Filled in circle
x<0Less than: Arrow to the left
Not Equal: Hollow circle
x>-5Greater than: Arrow to the right
Not Equal: Hollow circle
x≥8Greater than: Arrow to the right
Equal: Filled in circle
x<5 or x≥7Two 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=3This is not an inequality, but this equation is here to let you know what it looks like.

### Complexity=1, Mode=simple

Write the inequality described by the graph using 'x'. Sample answers: x>5, x<=-3, 3<x<7, x<-5 or x>5.
 1 2

### Complexity=1, Mode=and-or

Write the inequality described by the graph using 'x'. Sample answers: x>5, x<=-3, 3<x<7, x<-5 or x>5.
 1 2

### Complexity=1, Mode=simple

Write the inequality described by the graph using 'x'. Sample answers: x>5, x<=-3, 3<x<7, x<-5 or x>5.
1

2

### Complexity=1, Mode=and-or

Write the inequality described by the graph using 'x'. Sample answers: x>5, x<=-3, 3<x<7, x<-5 or x>5.