Solve the following inequation, write the solution set and represent on the number line. x+1 -3(x - 7) ≥ 15 - 7x > X€R [icse 2016]

Given that-

 3(x - 7) ≥3 15 - 7x > (x + 1)/3

=> - 3(x - 7)  ≥ 15 - 7x and 15 - 7x > (x + 1)/3

Case I

When - 3(x - 7) ≥ 15 - 7x

=>  - 3x + 21 ≥ 15 - 7x

Adding 7x - 21 on both sides, we get,

- 3x + 21 + 7x - 21  ≥  15 - 7x + 7x - 21

=> 4x  ≥ - 6

Dividing both sides by 4, we get,

(4x)/4  ≥  - 6/4

=> x  ≥ - 3/2

=>x  ≥  - 1.5

=> -1.5 ≤ x - - - - - - - (1)

 Case II 

15 - 7x > (x + 1)/3

Multiplying both sides by 3, we get,

3(15 - 7x) > x + 1

45 - 21x > x + 1

Adding both sides by 21x - 1, we get,

45 - 21x + 21x - 1 > x + 1 + 21x - 1

=>  44 > 22x

Dividing both sides by 22, we get

44/22 > 22/22 * x

=> 2 > x

=> x < 2. - - - - - - - - - (2)

combining (1) & (2),the solution set is

{x : - 1.5  ≤   x < 2, x ε{R}}

= [-1.5, 2)