Question

Solve each of the following inequalities
and illustrate the solution on a
number line.

a) 3y < -36
b) 4x < 28​

Answer 1

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}.