Given : A = {x : -8 5x + 2 17, x ∈ I} B = {x : -2 7 + 3x 17, x ∈ R} Where R = {real numbers} and I = {integers} Represent A and B on two different numbers lines. Write down elements of A ∩ B.

Question

KnowledgeBoat · Accepted Answer

Given, A = {x : -8 5x + 2 17, x ∈ I} Solving L.H.S. of the equation, ⇒ -8 5x + 2 ⇒ 5x -8 - 2 ⇒ 5x -10 ⇒ x -2 ......(i) Solving R.H.S. of the equation, ⇒ 5x + 2 17 ⇒ 5x 17 - 2 ⇒ 5x 15 ⇒ x 3 .......(ii) From (i) and (ii) we get, -2 x 3 Since, x ∈ I ∴ Solution set = {-1, 0, 1, 2, 3} Given, B = {x : -2 7 + 3x 17, x ∈ R} Solving L.H.S. of the equation, ⇒ -2 7 + 3x ⇒ 3x -2 - 7 ⇒ 3x -9 ⇒ x -3 .......(iii) Solving R.H.S. of the equation, ⇒ 7 + 3x 17 ⇒ 3x 17 - 7 ⇒ 3x 10 ⇒ x ........(iv) From (iii) and (iv) we get, -3 x A ∩ B = Elements common to both A and B, Hence, A ∩ B ={-1, 0, 1, 2, 3}.

Mathematics

Given : A = {x : -8 < 5x + 2 ≤ 17, x ∈ I}
B = {x : -2 ≤ 7 + 3x < 17, x ∈ R}
Where R = {real numbers} and I = {integers}
Represent A and B on two different numbers lines. Write down elements of A ∩ B.

Linear Inequations

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