Question

Which among the following inequality represents the interval [2, ∞)? (i) x − 3 ≥ 5, x ∈ (ii) 13x − 3 ≥ 5, x ∈ (1) (iii) 3x − 1 ≥ 3, x ∈ (iv)3x − 1 ≥ 5, x ∈ ​

Answer 1

Answer:

4 th is the correct answer of the given question

Answer 2

Answer:

(iv) 3x − 1 ≥ 5, x ∈ [2, ∞)

Step-by-step explanation:

Given :- The given equations are (i) x − 3 ≥ 5

                                                       (ii) 13x − 3 ≥ 5

                                                       (iii) 3x − 1 ≥ 3

                                                       (iv)3x − 1 ≥ 5

To Find :- Which of the given equations represents the interval [2, ∞).

Solution :-

(i) x − 3 ≥ 5  ⇒ x ≥ 5 + 3  ⇒ x ≥ 8, x ∈ [8, ∞)

(ii) 13x − 3 ≥ 5  ⇒ 13x ≥ 5 + 3  ⇒ 13x ≥ 8  ⇒ x ≥ 8/13  ⇒ x ≥ 0.62, x ∈ [0.62, ∞)

(iii) 3x − 1 ≥ 3  ⇒ 3x ≥ 3 + 1  ⇒ 3x ≥ 4  ⇒ x ≥ 4/3  ⇒ x ≥ 1.34, x ∈ [1.34, ∞)

(iv) 3x − 1 ≥ 5 ​ ⇒ 3x ≥ 5 + 1  ⇒ 3x ≥ 6  ⇒ x ≥ 2, x ∈ [2, ∞)

Therefore, in the equation 3x − 1 ≥ 5, x ∈ [2, ∞).

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