Final answer:
The inequality 5|t + 2| ≤ 20 is solved by dividing by 5 and considering the two scenarios of the absolute value, with the solution being the interval [-6, 2] in interval notation.
Step-by-step explanation:
To solve the inequality 5|t + 2| ≤ 20, you first divide both sides by 5, yielding |t + 2| ≤ 4. The absolute value inequality represents two scenarios: t + 2 ≤ 4 and t + 2 ≥ -4.
For the first scenario, subtracting 2 from both sides gives t ≤ 2. For the second scenario, subtracting 2 from both sides gives t ≥ -6. Combining these solutions, we get the interval -6 ≤ t ≤ 2.
Therefore, the solution in interval notation is [-6, 2].