{ LINEAR INEQUALITIES } CLASS 12 U.P. BORD निम्नलिखित प्रश्नो मेँ वास्तविक सख्या x के लिए हल कीजिए (A) 2x - 5 < x + 1 (B) 4x + 3 < 3x - 1 (C) X - 2 > 3 (D) 5x < 15 (E) -4x >_ -12

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]