If 2(3x - 4) - 2 < 4x - 2 ≥ 2x - 4; then the possible value of x can be where x ∈ N:

Concept:

Rules for Operations on Inequalities:

• Adding the same number to each side of an inequality does not change the direction of the inequality symbol.
• Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol.
• Multiplying each side of an inequality by a positive number does not change the direction of the inequality symbol.
• Multiplying each side of an inequality by a negative number reverses the direction of the inequality symbol.
• Dividing each side of an inequality by a positive number does not change the direction of the inequality symbol.
• Dividing each side of an inequality by a negative number reverses the direction of the inequality symbol.

Calculation:

Given: 2(3x - 4) -2 < 4x - 2 ≥ 2x – 4

First by solving the inequation: 2(3x - 4) -2 < 4x - 2 we get

⇒ 6x - 10 < 4x - 2

⇒ 2x < 8

⇒ x < 4--------(1)

Similarly, by solving the inequation 4x - 2 ≥ 2x - 4 we get

⇒ 2x ≥ - 2

⇒ x ≥ - 1--------(2)

From equation (1) and (2) we can say that -1 ≤ x < 4

So, out of the given options the possible value which x can take is 2.