To solve the inequality 1/2 (5r + 3) ≥ 14, we can start by isolating the variable r:
1/2 (5r + 3) ≥ 14
5r + 3 ≥ 28
5r ≥ 25
r ≥ 5
To solve the inequality -2s + 6 ≥ -8, we can isolate the variable s:
-2s + 6 ≥ -8
-2s ≥ -14
s ≤ 7
The two inequalities have a region of overlap where they are both true. This occurs when r is greater than or equal to 5 and s is less than or equal to 7. Therefore, the solutions that the inequalities have in common are:
r ≥ 5 and s ≤ 7