Question

Page : 1.6
Please answer with elaboration.

Answer 1

Here is the solution :

Q : 31 : |x-3| = 8 !..

A : 31 : |x-3| = 8,

=> x-3 = +8 or -8

=> x = +8+3 or -8+3

=> x = +11 or -5,

=> x = {-5,11} [This is the solution for x]

Option C is right !..



Q : 32 : Rational number between 1/2 and 3/4
A : 32 :

A rational number between a/b and c/d can be written as (a+c)/(b+d)

=> A rational number between 1/2 and 3/4 is 1+3/2+4 = 4/6 = 2/3,

=> One of the rational number is 2/3,

We can find more from this :

1/2 = 0.5,
3/4 = 0.75,

=> rational number between them are,
0.51, 0.52, 0.53,......,0.6,0.61,0.62,........0.7,0.71,.......0.74 ..... 0.75 !.

These are all the rational numbers between 1/2 and 3/4,


Therefore :
The answer for Q : 31 is Option C,

answer for Q : 32 is 2/3,

Hope you understand, Have a Great day !.
Thanking you, Bunti 360 !..

Answer 2

Hey friend, Harish here.

Here is your answer:

Given that,

1) x ∈ R,  So, x can be both positive and negative .

2) | x - 3 | = 8.

To find,

The values of x.

Solution:

CASE1:  Let x be positive

Then,  |x - 3| = 8

       ⇒ x = 8 + 3 = 11.

CASE 2: Let x be negative.

Then,  | -x -3 | = 8.

       ⇒ | - (x + 3) | = 8  (Here we took - as common).

Then now, we can remove the -ve symbols and absolute bracket because, any number in those brackets has a positive value.

Then, x + 3 = 8.

      ⇒ x = 8 - 3  = 5. ( But as it is a negative value it should be -5)

Therefore the values of x are { -5 , 11}. (OPTION - C).
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Hope my answer is helpful to you.