Solve the inequation :

3z - 5 ≤ z + 3 < 5z - 9; z ∈ R.

Graph the solution set on the number line.

Given,

3z - 5 ≤ z + 3 < 5z - 9

Solving L.H.S. of the above equation,

⇒ 3z - 5 ≤ z + 3

⇒ 3z - z ≤ 3 + 5

⇒ 2z ≤ 8

⇒ z ≤ 4 …..(i)

Solving R.H.S. of the above equation,

⇒ z + 3 < 5z - 9

⇒ 5z - z > 3 + 9

⇒ 4z > 12

⇒ z > 3 ……(ii)

From (i) and (ii) we get,

3 < z ≤ 4

∴ Solution set = {z : 3 < z ≤ 4, z ∈ R}.

Solution on the number line is :