2. Solve the following inequalities and draw the solution set on a number line.
(i) x + 3 > 8 given that x e W
(ii) 3 - 2x2 X-12, given that x e N.
(iii) 2 (3x - 1)x 16, xe N.
(iv) 3x < 6, X e Z.
Answers
Step-by-step explanation:
The given inequality is 24x < 100
=> x < 100/24
=> x < 25/6
(i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than 25/6
Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3, and 4.
4:
Solve 3x + 8 > 2, when (i) x is an integer (ii) x is a real number
Answer:
The given inequality is 3x + 8 > 2
=> 3x + 8 – 8 > 2 – 8 [8 is subtracted both sides]
=> 3x > -6
=> x > -6/3
=> x > -2
(i)The integers greater than –2 are –1, 0, 1, 2, ...
Thus, when x is an integer, the solutions of the given inequality are –1, 0, 1, 2 ...
Hence, in this case, the solution set is {–1, 0, 1, 2, ...}.
(ii) When x is a real number, the solutions of the given inequality are all the real numbers,
which are greater than –