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101.

Solution of a linear inequality in variable x is represented on number line(i) (A) x ∈ (– ∞, 5) (B) x ∈ (– ∞, 5](C) x ∈ [5, ∞,) (D) x ∈ (5, ∞)(ii)(A) x ∈(9/2, ∞)(B) x ∈ [9/2, ∞)(C) x ∈ [– ∞, 9/2)(D) x ∈ (– ∞, 9/2](iii)(A) x ∈ (– ∞, 7/2)(B) x ∈ (– ∞,7/2](C) x ∈ [7/2, – ∞)(D) x ∈ (7/2 , ∞)(iv)(A) x ∈ (– ∞, – 2)(B) x ∈ (– ∞, – 2](C) x ∈ (– 2, ∞](D) x ∈ [– 2, ∞)

Answer»

(i) (D) x ∈ (5, ∞)

(ii) (B) x ∈ [9/2, ∞)

(iii) (A) x ∈ (– ∞, 7/2)

(iv) (B) x ∈ (– ∞, – 2]
Discussion
102.

Solve: 3(2 – x) > 2(1 – x)

Answer»

Given 6 – 3x > - 2x + 3x

⇒ 6 – 2 > - 2x + 3x

⇒ 4 > x.

∴ Solution set = (-∞,  4]
Discussion
103.

Solve: x + x/2 + x/3 < 11

Answer»

Given: (6x + 3x + 2x)/6 < 11

11x < 11 x 6 = 66

∴ x < 66/11 = 6
Discussion
104.

A = {\(x\) :11\(x\) - 5 &gt; 7\(x\) + 3, \(x\) ∈ R} and  B = {\(x\) : 18\(x\) – 9 &gt; 15 + 12\(x\), \(x\) ∈ R}.The range of the set A ∩ B is (a) [– ∞, 4](b) (0, 4) (c) [4, ∞] (d) (– 4, 4)

Answer»

(c) [4, ∞)

A = {\(x\) : 11\(x\) – 5 > 7\(x\) + 3, \(x\) ∈ R} 

⇒ 11\(x\) – 5 > 7\(x\) + 3     ⇒ 4\(x\) > 8 ⇒ \(x\) > 2 

⇒ A = {\(x\) : \(x\) > 2, \(x\) ∈ R} 

B = {\(x\) : 18\(x\) – 9 > 15 + 12\(x\), \(x\) ∈ R} 

⇒ 18\(x\) – 9 > 15 + 12\(x\) ⇒ 6\(x\) > 24 ⇒ \(x\) > 4 

⇒ B = {\(x\) : \(x\) > 4, \(x\) ∈ R} 

∴ A ∩ B = {\(x\) : \(x\) > 2, \(x\) ∈ R} ∩ {\(x\) : \(x\) > 4, \(x\) ∈ R} 

⇒ \(x\) > 4 ⇒ x∈ [4, ∞).
Discussion