Solve each of the following inequalities
and illustrate the solution on a
number line.
a) 3y < -36
b) 4x < 28
Answers
Step-by-step explanation:
The given inequality is 24x < 100.
(i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than.
Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3, and 4.
Hence, in this case, the solution set is {1, 2, 3, 4}.
(ii) The integers less than are …–3, –2, –1, 0, 1, 2, 3, 4.
Thus, when x is an integer, the solutions of the given inequality are
…–3, –2, –1, 0, 1, 2, 3, 4.
Hence, in this case, the solution set is {…–3, –2, –1, 0, 1, 2, 3, 4}.
Page No 122:
Question 2:
Solve –12x > 30, when
(i) x is a natural number (ii) x is an integer
ANSWER:
The given inequality is –12x > 30.
(i) There is no natural number less than.
Thus, when x is a natural number, there is no solution of the given inequality.
(ii) The integers less than are …, –5, –4, –3.
Thus, when x is an integer, the solutions of the given inequality are
…, –5, –4, –3.
Hence, in this case, the solution set is {…, –5, –4, –3}.
