Question

Solve the inequality -3 ≤ 4 -7x/2 ≤ 18

Answer 1

Given :   -3 ≤ 4 -7x/2 ≤ 18

To find :   x

Solution:

-3 ≤ 4 -7x/2 ≤ 18

Lets break this into two

-3 ≤ 4 -7x/2

& 4 -7x/2 ≤ 18

-3 ≤ 4 -7x/2

=> -6 ≤ 8 - 7x

Adding 7x on both sides

=> 7x - 6 ≤ 8

=> 7x ≤ 14

=>  x ≤ 2

4 -7x/2 ≤ 18

=> 8 - 7x ≤  36

=> 8 ≤  36 + 7x

=> -28 ≤ 7x

=> - 4 ≤ x

=> x ≥ - 4

- 4  ≤ x  ≤ 2

=> x ∈ [ - 4 , 2 ]

x ∈ [ - 4 , 2 ]

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