Introduction to Inequalities

Inequalities use four symbols

< Less than
> Greater than
Less than or equal to
Greater than or equal to

An inequality such as x<5 has many answers. In this example, any number that is less than 5 would make this statement true. Thus, there are many numbers that are part of the answer. Let's list a few: 4.9, 4.8, 4.5, 4, 3, 2, 1.99, 1.5, 0, -1, -2, -2.56 and so many more.

The difference between x<5 and x ≤ 5 is that x<5 does not include the 5 itself because 5 is not less than 5. However, x ≤ 5 does include the 5 because it is looking for any number less than or equal to 5.

Let's look at a few examples and determine whether or not the number 10 would be part of the solution.
1)x>3 Yes, 10 is part of the solution because it is greater than 3.
2)y<7 No, 10 is not part of the solution because it is not less than 7.
3)y<10No, 10 is not part of the solution because 10 is not less than 10
4)x≥10 Yes, 10 is part of the solution because 10 is equal to 10 and the symbol used is greater than or equal to.
5)y≤ -9 No, 10 is not less than or equal to -9


Practice:Tell whether or not the number 2 is part of the solution.

1) y>1

2) x<10

3) y ≤ 2

4) x ≥ -3

5) x>2

Answers: 1) yes 2) yes3) yes4) yes5) no

Related Links:
Math
Algebra
Inequalities
Algebra Topics
Graphing linear inequalities
Solving inequalities with addition
Solving inequalities with multiplication/division
Solving multi-step inequalities
Solving Inequalities


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