Question

Given : A = {x:3 < 2x-1<9,XER} , B = {x:11 5 3x + 2 5 23,X E R}
where R is the set of real numbers.
(1) Represent A and B on number lines
(ii) On the number line also mark ANB.​

Answer 1

A = { 3 , 4 } , B = { 3 , 4 , 5 , 6 , 7 }

Step-by-step explanation:

A = {x: 3 < 2x-1 < 9, X ∈ R} ,

3 < 2x-1

=> 4 < 2x

=> 2 > x

2x-1 < 9

=> 2x < 10

=> x < 5

=>  2 < x < 5

=> A = { 3 , 4 }

11 ≤ 3x + 2 ≤ 23,

B = {x: 11 ≤ 3x + 2 ≤ 23, X ∈ R} ,

11 ≤ 3x + 2

=> 9 ≤ 3x

=> 3 ≤ x

3x + 2 ≤ 23

=>  3x  ≤ 21

=> x ≤ 7

3 ≤ x  ≤ 7

=> B = { 3 , 4 , 5 , 6 , 7 }

A ∩ B = { 3 , 4 }

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

A = {x: 3 < 2x-1 < 9, X ∈ R} ,

3 < 2x-1

=> 4 < 2x

=> 2 > x

2x-1 < 9

=> 2x < 10

=> x < 5

=> 2 < x < 5

=> A = { 3 , 4 }

11 ≤ 3x + 2 ≤ 23,

B = {x: 11 ≤ 3x + 2 ≤ 23, X ∈ R} ,

11 ≤ 3x + 2

=> 9 ≤ 3x

=> 3 ≤ x

3x + 2 ≤ 23

=> 3x ≤ 21

=> x ≤ 7

3 ≤ x ≤ 7

=> B = { 3 , 4 , 5 , 6 , 7 }

A ∩ B = { 3 , 4 }