Because it is a system of inequalities, the common solution of the system, namely a set of integer values, has to satisfy both the inequalities, simultaneously.

Let's solve the first one:

5< 2x-3

In order to isolate x values, we have to add the value "+3", both sides of the inequality:

5+3 < 2x-3+3

8 < 2x

We'll divide by 2 both sides:

8/2 < x

4 < x

Because x is an integer number, it will have values bigger than 4, namely{5,6,7...}.

Now, we'll solve the second inequation:

2x-3 ≤ 14

We'll add the value "+3", both sides of the inequality:

2x-3+3 ≤ 14+3

2x≤ 17

We'll divide by 2 both sides:

x≤ 17/2

x≤ 8.5

Because x is an integer number, it will have values till 8.

Because of the fact that it is about a system of inequations and the solution has to satisfy both, the common solution will be the common values found in the set of values found for the both inequalities, which are {5,6,7,8}.

**So x belongs to the set {5,6,7,8}.**

5 <2x-3<14 and z belongs to integer.

Solution:

Add 3 to the inequalities.

5+3<2x<14+3

8<2x<17.

Divide by 2

4 <x< 17/2 = 8.5

4 <x < 9 in integer.