To solve ∣3x−4∣≤5, we should consider two scenarios for the absolute value: 3x−4≤5 and 3x−4≥−5.
1. Solving 3x−4≤5:
3x−4≤5
Add 4 to both sides:
3x≤9
Divide both sides by 3:
x≤3
2. Solving 3x−4≥−5:
3x−4≥−5
Add 4 to both sides:
3x≥−1
Divide both sides by 3:
x≥−31
Combining both results, we have −31≤x≤3, which is the correct answer.
Answer:
−31≤x≤3