Final answer:
To solve the inequality 22q + 73 > 52q + 63, subtract 22q from both sides, then subtract 63, and finally divide by 30 to isolate q, resulting in q < 1/3.
Step-by-step explanation:
To solve the inequality 22q + 73 > 52q + 63, we must first eliminate terms wherever possible to simplify the algebra. We can begin by subtracting 22q from both sides to get:
73 > 30q + 63
Next, we subtract 63 from both sides:
10 > 30q
Then we divide both sides by 30 to isolate q:
q < 1/3
This tells us that q must be less than one-third. When checking if this answer is reasonable, we recognize that one-third is indeed less than the whole, which is consistent with the initial inequality.