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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 Number Lines. Write Down the Elements of a ∩ B. - ICSE Class 10 - Mathematics

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Question

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 number lines. Write down the elements of A ∩ B.

Solution

`A = {x :-8 < 5x + 2  <= 17,  x ∈ I}`

= {x :-10 < 5x <= 15, x  ∈ I}

`= {x : -2 < x <= 3, x ∈ I}`

It can be represented on number line as

B = {x : -2 <= 7 + 3x < 17, x ∈ R}

= {x : 9 <= 3x < 10, x ∈ R}

`={x : -3 <= x < 3.33, x ∈ R}`

it can be represeneted on number line as

A ∩ B = {-1, 0, 1, 2, 3}

  Is there an error in this question or solution?

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Solution 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 Number Lines. Write Down the Elements of a ∩ B. Concept: Representation of Solution on the Number Line.
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