Inequalities

An inequality is a statement that two expressions are not equal.

The notation a < b means that a is less than b.
The notation a > b means that a is greater than b.
The notation a ≠ b means that a is not equal to b
The notation a ≤ b means that a is less than or equal to b The notation a ≥ b means that a is greater than or equal to b 

Symbols

 Inequality Statement  Equation
 x is at least 3  x ≥ 3
 y is at most 9  y <= 9
 z is between 2 and 4  2 < z < 4
 x is less than 3  X < 3
 y is more than 9  Y > 9

 

 

 

 

 

 

You can solve inequalities in the same way you can solve equations, by following these rules:

You may add any positive or negative number to both sides of an inequality. You may multiply or divide both sides of an inequality by any positive number.

Inequalities Properties (Help)

Inequalities Graphs (Help)

Inequalities (Vocabulary)

Inequalities (Writing)

One Step Inequalities

Two Step Inequalities

Linear Inequalities

Inequalities Word Problems

Graphing Inequalities on Number Lines.

The graph of a linear inequality in one variable is a number line. When we graph an inequality on a number line we use open and closed circles to represent the number. The open circle means the number is not included in the solution NL1

 

X>5 means that whatever value x has, it must be greater than 5. The open dot shows that 5 is not a solution. Numbers greater than 5 are to the right of 5 on the number line.

NL2

 

 

 

The closed circle means the number is included in the solution.       X ≥ 5 means that whatever value x has, it must be greater than or equal to 5

NL2

 

 

 

Numbers less than 5 are to the left of 5 on the number line.     X<5 means x can be any value less than 5

 

Reversal property of inequality

ine2

 

 

 

 

 

 

 

  If  a < b    then    b > a

 

INE1

 

 

 

 

 

 

 

 

Book

 

 

 

 

 

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