Question

Solve 24x < 100, when

(i) x is a natural number

(ii) x is an integer

Solution

24x < 100 $rightwards double arrow$ $fraction numerator 24 straight x over denominator 24 end fraction less than 100 over 24 space rightwards double arrow space straight x less than 25 over 6 space or space straight x less than 4 1 over 6$
∴ (i) When $space space straight x space element of space straight N comma space straight x space equals space 4 comma space 3 comma space 2 comma space 1$
∴ Solution set is $WiredFaculty$
(ii) When $straight x space element of space straight Z comma space straight x space equals space 4 comma space 3 comma space 2 comma space 1 comma space 0 comma space minus 1 comma space minus 2 comma space minus 3......$
The solution set is $open curly brackets.... comma negative 3 comma space minus 2 comma space minus 1 comma space 0 comma space 1 comma space 2 comma space 3 comma space 4 close curly brackets$

Question

Wired Faculty App

Solve -12x > 30, when

(i) x is a natural number. (ii) x is an integer.

Solution

-12x > 30
$rightwards double arrow$ $fraction numerator negative 12 straight x over denominator negative 12 end fraction less than fraction numerator 30 over denominator negative 12 end fraction$ (∵ -12 < 0)
$rightwards double arrow$ $WiredFaculty$
∴ (i) When $straight x space element of space straight N$ , there is no solution
∴ The solution set is $straight ϕ$ .
(ii) When $WiredFaculty$
The solution set is $WiredFaculty$

Question

Wired Faculty App

Solve 5x – 3 < 7, when

(i) x is an integer. (ii) x is a real number.

Solution

5x – 3 < 7
5x – 3 < 7 $rightwards double arrow$ 5x < 10 $rightwards double arrow$ x<2
∴ (i) When $space space straight x element of space straight Z comma space straight x space equals space 1 comma space 0 comma space minus 1 comma space minus 2 comma space........$
The solution set is $open curly brackets.... comma space minus 3 comma space minus 2 comma space minus 1 comma space 0 comma space 1 close curly brackets$
(ii) When $straight x space element of space straight R comma space space straight x less than 2 space or space straight x space element of space left parenthesis negative infinity comma space 2 right parenthesis$
∴ The solution set is $space space left parenthesis negative infinity comma space 2 right parenthesis$

Question

Wired Faculty App

Solve 3x + 8 > 2, when

(i) x is an integer. (ii) x is a real number.

Solution

3x + 8 > 2
$rightwards double arrow$ 3x > 2 - 8 $rightwards double arrow$ 3x > - 6 $rightwards double arrow$ x > -2
∴ (i) When $space space straight x element of space straight Z comma$
x = -1, 0, -1, 2, 3, ........
The solution set is $open curly brackets negative 1 comma space 0 comma space 1 comma space 2 comma space 3 comma......... close curly brackets$
(ii) When $straight x space element of space straight R space rightwards double arrow space straight x greater than negative 2 space space or space straight x space element of space left parenthesis negative 2 comma space infinity right parenthesis$
The solution set is $WiredFaculty$