Final answer:
To solve the inequality 4p - 7 ≥ 9p + 8, we solve for p and determine that p must be greater than or equal to -3. Upon checking the values in set S: {−2, −3, −4, −5}, we find that -2 and -3 satisfy the inequality.
Step-by-step explanation:
We are given the inequality 4p − 7 ≥ 9p + 8. To determine which integers from the set S: {−2, −3, −4, −5} satisfy this inequality, we need to solve for p first and then check which values from the set work.
Let's solve the inequality step by step:
Subtract 4p from both sides: −7 ≥ 5p + 8.
Subtract 8 from both sides: −15 ≥ 5p.
Divide both sides by 5: −3 ≥ p.
This means that for the inequality to hold true, p must be greater than or equal to −3. Now we can determine which integers in set S {−2, −3, −4, −5} meet this condition.
−2 and −3 satisfy the inequality because they are greater than or equal to −3.
−4 and −5 do not satisfy the inequality because they are less than −3.
Therefore, the correct answer is S: {−2, −3}.