Solve the following inequation and represent the solution set on a number line.(-8*1/2)< -1/2 -4x<=7*1/2 ; x€I [icse 2017]

Solve the following inequation and represent the solution set on a number line:

- 8*1/2 < - 1/2 - 4x ≤ 7 *1/2 , , x εI

Solutions:

Given that:- 

-8 *1/2 < - 1/2 - 4x≤7 *1/2

⇒ Convert mixed fractions to improper fractions:

- 17/2 < - 1/2 - 4x ≤15/2

Adding 1/2 to each term, we get:

- 17/2 + 1/2 < - 4x ≤ 15/2 + 1/2

Simplify the fractions:

- 16/2 < - 4x ≤16/2

=> - 8 < - 4x ≤ 8

Dividing each term by -4, we get:

2 > x >= - 2

[Sign reverses when each term is divided by same negative number]

We can write it as

- 2 ≤ x < 2

The solution set is {x:  - 2 ≤ x < 2; x Ɛ I}

= {-2,-1,0,1}