x + 7 > 3 and x – 5 ≤ –1

Sure, let's solve this step by step:

The given inequalities are: x + 7 > 3 and x – 5 ≤ –1

Let's solve the first inequality:

x + 7 > 3

Subtract 7 from both sides:

x > 3 - 7

So, x > -4

Now, let's solve the second inequality:

x - 5 ≤ -1

Add 5 to both sides:

x ≤ -1 + 5

So, x ≤ 4

Therefore, the solution to the system of inequalities is -4 < x ≤ 4.