Page 37 - Mathematics

Solution
11 3
x
2
(a) 2−≤ x ≤ 2 (b) − <≤ (c) x <− 1 or x ≥ (d) 1 x−< < 2
4 2

Example 2.18 Tanzania Institute of Education

Represent on a number line all the real numbers between 0.3−  and 2.

Solution
Let x be a set of real numbers between 0.3−  and 2. This set of real numbers

can be represented as 0.3 x−  << 2 since, both 0.3−  and 2 are not included
in the set. The number line representing this set of real numbers is shown in
the following number line.

-0.3 < x < 2

Exercise 2.6

1. Represent each of the following numbers on a number line.
(a) 4,− − 2, 0, 2, 4

(b) 2−≤ k ≤ 1 where k is a real number
(c) 5− < y ≤− 2, where y is a real number
(d) 2−< x < 4, where x is a real number
2. Represent each of the following integers on a number line under the
given conditions.
3
5
(a) 6− < a <− 2 (c) c < and c >− (e) f >− 9 and f ≤− 4.
3 e ≤
1
b
(b) 4− < <− (d) −≤ 5
3. Draw a number line to represent each of the following real numbers.
1
(a) x <− 1 or x >
2 Mathematics Form One
(b) 6− ≤ x and x ≤− 2
4. Use a number line to determine the distance between 3− and 2.

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