Chapter 8 Inequalities

Learning Objectives
1 understand the meanings of inequality signs.
equal to, greater than, less than, greater than or equal to, less than or equal to
2 explore the fundamental properties and some laws of equalities.
3 solve simple linear inequalities in one unknown and represent the solution on a
number line.

Title page story, oral and dictation
Tom, Kent and Butt are going to a restaurant for dinner which will cost them a total
of $300. Kent has got not less than $80 and Butt has got not more than $100. At least how much should Tom have in order to pay the bill? $220

Hints
1 When paying the bill, Tom has found that Butt has no money. Do you think Butt is
lying? Explain briefly.
$0 is not more than $100
2 Suppose Butt is not lying, at least how much do Kent and Butt have in total?
$80 + $0 = $80

Preview
Basic knowledge
The order of numbers on a number line

Basic technique
1 Multiplication and division of directed numbers
2 Solving linear equation in one unknown
8.1 Inequalities
An inequality is an expression connecting two expressions with an inequality sign.
For an inequality involving x as an unknown, any value of x which satisfies the
inequality is called a solution of the inequality.
8.2 Graphical Representations of Inequalities

8.3 Basic Properties of Inequalities
For any two numbers a and b, they must have one of the following relations.
a is less than b, a=b, or a is greater than b, this is called the trichotomy
property.
If a is greater than b, then
a+c is greater than b+c
a-c is greater than b-c, this is called the additive property.
If a is greater than b and c is a positive number, then ac is greater than bc.
a=2 b=1 c=3 2x3 is greater than 1x3, 6 is greater than 3
If a is greater than b and c is a negative number, then ac is less than bc
a=2 b=1 c=-3 2x-3 is less then 1x-3, -6 is less than -3
multiplicative property

8.4 Linear Inequalities in One Unknown
8.5 Applications of Inequalities

**Chapter Summary
Term Introduced
not equal to, greater than, less than, greater than or equal to, less than or equal
to

Fact to Remember
1 Graphical representation of inequalities
2 Trichotomy property
3 Transitive property
4 Additive property
5 Multiplicative property

Additional Questions

Repeat and check carefully again
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