Mathematics If −2≤ 1 2 − 2x 3 ≤1 5 6 ,x∈N then find the solution set.

$If − 2 ≤ 12 − 2 x 3 ≤ 156, x ∈ N$ then find the solution set.

A
$− 115 ≤ x ≤ 154$
B
$− 114 ≤ x ≤ 154$
C
$− 94 ≤ x ≤ 154$
D
$− 114 ≤ x ≤ 34$

Solution:

Given,

− 2 ≤ 12 − 2 x 3 ≤ 156, x ∈ N

.
The range of x from given is,

− 2 ≤ 12 − 2 x 3 ≤ 156 ⇒ − 2 − 12 ≤ − 2 x 3 ≤ 156 ⇒ − 52 ≤ − 2 x 3 ≤ 116 ⇒ − 15 ≤ − 4 x ≤ 11

On further simplification,

⇒ − 154 ≤ − x ≤ 114 ⇒ − 114 ≤ x ≤ 154

Therefore, the range for value of x is

− 114 ≤ x ≤ 154

.
The correct option is 2).

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