Let A = x ∈ ℝ : x + 3 + x + 4 ≤ 3 , B = x ∈ ℝ : 3 x ∑ r = 1 ∞ 3 10 r x - 3 < 3 - 3 x , where [ t ] denotes greatest integer function. Then,

Step-by-step solution

Given, A = x ∈ ℝ : x + 3 + x + 4 ≤ 3   &   B = x ∈ ℝ : 3 x ∑ r = 1 ∞ 3 10 r x - 3 < 3 - 3 x , Now solving A we get, x + 3 + x + 4 ≤ 3 ⇒ x + 3 + x + 4 ≤ 3 ⇒ 2 x ≤ - 4 ⇒ x ≤ - 2 ⇒ x < - 1 ⇒ A = - ∞ , - 1 Now solving B we get, 3 x ∑ r = 1 ∞ 3 10 r x - 3 < 3 - 3 x Now using infinite G . P formula S ∞ = a 1 - r we get, ⇒ 3 x 3 · 1 10 1 - 1 10 x - 3 < 3 - 3 x &#8