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.
We can use a number line to represent inequalities.
If the number is “included” we draw a solid circle, as the start point.
If the number is “not included” we draw an empty circle, as the start point.
The arrow an the other side of the line means that the solution set extends in the direction shown.
X ≥ 4, means that X can equal any number greater than or equal to 4 (the value of X could be 4, 5, 6, 7, 8, and so on). This is an example of an unbounded set, the set of all numbers greater than or equal to 4. The closed circle in the graph indicates that 4 is a member of the solution set.
Bounded Inequalities.
An inequality can fall between two numbers, such as X ≥ 1 and  X ≤6
(the value of X could be 1, 2, 3, 4, 5, or 6)
 

 

 

IQ02       Linear_Inequalities

IQ03       One_Step_Inequalities

IQ04       Two_Step_Inequalities

IQ01       Inequalities_Word Problems

 

 

Inequalities Properties (Help)

Inequalities Graphs (Help)

Inequalities (Vocabulary)

Inequalities (Writing)

 

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

 

 

 

 

 

 

 

 

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