Solve and graph the solution set of :

2x - 9 < 7 and 3x + 9 ≤ 25; x ∈ R.

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,

⇒ x ≤ $5\dfrac{1}{3}$

∴ Solution set = {x : x ≤ $5\dfrac{1}{3}$ and x ∈ R}.

Solution on the number line is :