Final answer:
To solve the system, isolate r in each inequality: r/4 < -5 implies r < -20, and -2r - 7 <= 3 leads to r >= -5. The solution is r < -20 or r >= -5.
Step-by-step explanation:
To solve the system of inequalities r/4 < -5 or -2r - 7 ≤ 3, we first isolate r in each inequality.
For the first inequality:
r/4 < -5
Multiply both sides by 4 to get r < -20.
For the second inequality:
-2r - 7 ≤ 3
First, add 7 to both sides: -2r ≤ 10
Then, divide both sides by -2, remembering to reverse the inequality: r ≥ -5.
The solution to the system of inequalities is that r is either less than -20 or greater than or equal to -5.