Page 31 - Mathematics

In general, mathematical statements which use ,≠ > , ,< ≥ or ≤ are called inequalities.
,

Note:

1. The sharp end of > and < always points to a smaller number.
2. The symbols ≤ and ≥ are sometimes referred to as at most and at least,
respectively. Tanzania Institute of Education
3. If the inequality is divided or multiplied both sides by a negative number,
the direction of the inequality sign changes.

Suppose a, b, and c are real numbers which are represented on the number line
shown in the following number line:

a b c
Generally, on a number line, a number to the right side of another number is always
greater than a number to its left side. Thus, from the number line,
b is greater than a, which can also be written as b > . a
c is greater than b, which can also be written as c > . b
The vice versa is also true, that is, a number which is on the left side of another
number on a number line is always less than the number on its right side. That is,
ab< and bc< .

Example 2.12

Study the following number line and use inequality symbols to answer the
questions that follow.

(a) Write all real numbers which are greater than zero.
(b) Write all real numbers which do not exceed 2.
(c) Write all real numbers between –3 and 4.

Solution
(a) Let x be any real number that is greater than 0. The symbol > is used to Mathematics Form One
represent the solution. There are infinity real numbers which are greater
than zero. Therefore, x > 0.

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