Question

Exercise 6.3
Find the solution set of the following equations. Also verify th,
VI. 4x - 5 =1/3x +7 2. 3/y = 2 3. JZ - 8 = 1 4.
Vy
3
6. 25y- 6 = 4 Ny + 3
7./12 -
W 4y + 2 + 13
5.
-= 2
6
8. Vy - 7 = -4 4
9. VX-1 = 8
10.
10.3/1+​

Answer 1

Answer:

Question 1:

Solve 24x < 100, when (i) x is a natural number (ii) x is an integer

Answer:

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.

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}.

Question 2:

Solve –12x > 30, when (i) x is a natural number (ii) x is an integer

Answer:

The given inequality is –12x > 30

=> -x > 30/12

=> -x > 5/2

=> x < -5/2

(i) There is no natural number less than (-5/2).

Thus, when x is a natural number, there is no solution of the given inequality.

(ii) The integers less than -5/2 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}.