Page 32 - Mathematics

(b) Let x be any real number which does not exceed 2. Numbers on the left
side of 2 on a number line are always less than 2. Also, 2 is included as
it satisfies the given condition. Thus, the less than or equal inequality

symbol should be used to present the solution. Therefore, x ≤ 2.
(c) Let x be a real number between 3− and 4. This means that 3−< x and

x
x < 4. Combining the two inequalities gives, 3−< < 4.

Example 2.13

Tanzania Institute of Education
If x is an integer, locate each of the following on a number line.
(a) 1− is less than x and x is less than 4.
(b) 2− is less than or equal to x and x is less than or equal to 6.

Solution

(a) The statement is equivalent to 1−< x < 4, where x is an integer. On a
number line, it is represented as follows:

(b) The statement is equivalent to 2−≤ ≤ 6, where x is an integer. On a
x
number line, it is represented as follows:

Example 2.14

Use a number line to compare each of the following pair of numbers.
Mathematics Form One Solution
(a) 0.54 and 0.33
and 0.33−
(b) 0.54−

(a) 0.54 and 0.33 are represented in the following number line.

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