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.

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 < $\dfrac{10}{3}$ ……..(iv)

From (iii) and (iv) we get,

-3 ≤ x < $\dfrac{10}{3}$

A ∩ B = Elements common to both A and B,

Hence, A ∩ B ={-1, 0, 1, 2, 3}.