Question

If x ∈ R, the solution set of 6 ≤ – 3 (2x – 4) < 12 is ______.

Options

• {x : x ∈ R, 0 < x ≤ 1}

• {x : x ∈ R, 0 ≤ x < 1}

•  {0, 1}

• none of these

Answer 1

If x ∈ R, the solution set of 6 ≤ – 3 (2x – 4) < 12 is {x : x ∈ R, 0 < x ≤ 1}.

Explanation:

x ∈ R

6 ≤ – 3(2x – 4) < 12

⇒ 6 ≤ – 3(2x – 4)

⇒ 6 ≤ – 6x + 12

⇒ 6 ≤ 12 –6

⇒ 6x ≤ 6

⇒ `x ≤ (6)/(6)`

⇒  x ≤ 1                 ...(i)
and

–3(2x – 4) < 12

⇒ –6x + 12 < 12

⇒ –6x < 12 – 12

⇒ –6x < 0

⇒ x < 0                  ...(ii)

From (i) and (ii),

∴ 0 < x ≤ 1

Solution set = {x : x ∈ R < x ≤ 1}