For this case we must find the solution set of the given inequalities:
Inequality 1:
[tex]x + 2 <5[/tex]
Subtracting 2 from both sides of the inequality we have:
[tex]x <5-2\\x <3[/tex]
Thus, the solution is given by all values of x less than 3.
Inequality 2:
[tex]x-7> -6[/tex]
Adding 7 to both sides of the inequality we have:
[tex]x> -6 + 7\\x> 1[/tex]
Thus, the solution is given by all values of x greater than 1.
Therefore, the solution set is given by all real numbers.
Answer:
All real numbers
