Page 30 - Mathematics

Inequalities in real numbers

In daily life, people are faced with problems related to comparing quantities of the
same item for the purpose of making decisions. Consider the following examples:
(i) In some places, the speed of the car is limited to a certain maximum value
due to the large number of pedestrians.
(ii) Event organisers can set a maximum number of attendees for the event.
(iii) Most banks limit the withdrawal amount to a certain minimum and maximum
amount per day in automated teller machines.
(iv) In schools, a minimum pass mark is set for students to be awarded certificates
of completion of education.
Activity 2.5 guides you in comparing quantities in real life.
Tanzania Institute of Education

Activity 2.5: Comparing quantities in real life

1. Measure the lengths, widths, and heights of different objects of your choice.
2. Compare the measured values of a pair of objects in task 1.

In Mathematics, an inequality is a statement that compares or relates two values or
expressions. The common terms involved in comparing the values or expressions
are “less than”, “greater than”, “greater than or equal to”, “less than or equal to”, or
“not equal to”. For instance, the following statements are examples of inequalities:

(i) − 5 is less than 0.
(ii) John’s age is greater than Jane’s age.
(iii) x is less than or equal to 9.
(iv) y is greater than or equal to 0.
(v) 2.5 is not equal to 1.2.
The mathematical statements can be written using symbols which represent
inequalities as shown in the following table. Example

Inequality symbols
Word
Mathematics Form One Less than < John’s age > Jane’s age
−
50<
Greater than
>
Less than or equal
x ≤
9
≤

Greater than or equal
y ≥
0
≥
Not equal to
≠
24 2.5 ≠ 1.2

25/10/2024 09:51:07
Mathematics form 1.indd 24
Mathematics form 1.indd 24 25/10/2024 09:51:07