Hi Vipin,
(A) 2x - 5 < x + 1
2x - 5 - x < 1
2x - x < 1 + 5
x < 6
So, x is a real number less than 6.
x ∈ (-∞, 6)
(B) 4x + 3 < 3x - 1
4x + 3 - 3x < -1
4x - 3x < -1 - 3
x < -4
So, x is a real number less than -4.
x ∈ (-∞, -4)
(C) x - 2 > 3
x > 3 + 2
x > 5
So, x is a real number greater than 5.
x ∈ (5, ∞)
(D) 5x < 15
x < 15/5
x < 3
So, x is a real number less than 3.
x ∈ (-∞, 3)
(E) -4x ≥ -12
Multiplying -1 both sides, (when we multiply by -1, sign of equality reverses)
-1 × (-4x) ≤ -1 × -12
4x ≤ 12
x ≤ 12/4
x ≤ 3
So, x is a real number less than or equal 3.
x ∈ (-∞, 3]
Written on May 5, 2017, 1:41 p.m.