SS1 Third Term Further Mathematics Lesson Note – Inequalities

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WEEK 8                                                                                                                                                                     

TOPIC: INEQUALITIES

CONTENT:

• Notation and basic rules of inequalities
• Linear inequalities in one variable
• Absolute values
• Inequalities in two variables
• Graphs of linear inequalities in two variables.

Notation and basic rules of inequalities

Symbols commonly used for inequalities include;

< means less than

> means greater than

≥ greater than or equal to

≤ less than or equal to

We use the word ‘inequal’ or ‘unequal’ when comparing two variables. For example 5 is not equal to 4, then we say that 5 is greater than 4. And we write with the symbol 5 > 4.

3 is less than 8 and we write as 3 < 8.

In general, a > b or b < a. Some other times if a is greater than b or a is equal to b then we write as a ≥ b or b ≤ a. This means a is greater or equal to b or b is less or equal to a’

On the number line, 0 is called the reference point. Points to the right are positive and points to the left are negative. 5 is on the right of 3. Then 5 > 3 or 5 > 3. The information can be presented as 5 -3 > 0 or 3 -5 < 0. This can be represented on the number line.

The arrow represents the solution set of 5 > 3. Note that the point 3 and 5 are not included in the solution.

If x > 4 then this can be represented as below:

The small circles on 4 and 2 shows that both are not included.

The basic rules of inequalities are as follows:

1. (a) If a  > b and c > 0 then a + c > b + c

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