Solve and graph the solution set of :

2x - 9 ≤ 7 and 3x + 9 > 25; x ∈ I

Given,

2x - 9 ≤ 7 and 3x + 9 > 25

Solving, 2x - 9 ≤ 7

⇒ 2x ≤ 7 + 9

⇒ 2x ≤ 16

⇒ x ≤ 8 ………(i)

Solving, 3x + 9 > 25

⇒ 3x > 25 - 9

⇒ 3x > 16

⇒ x > $\dfrac{16}{3}$

⇒ x > $5\dfrac{1}{3}$ ……..(ii)

From (i) and (ii) we get,

⇒ $5\dfrac{1}{3} \lt x \le 8$

Since, x ∈ I,

∴ Solution set = {6, 7, 8}.

Solution on the number line is :