Final answer:
The inequality representing the range of possible lengths for a TV show produced for an hour-long slot, varying by 2.5 minutes, is 39.5 ≤ x ≤ 44.5, where x is the actual length of the TV show.
Step-by-step explanation:
To find the range of lengths that the TV show could be, we will use the information provided: the TV show is typically 42 minutes in length, but may vary by as much as 2.5 minutes. Let x be the actual length of the TV show.
The range can be found by considering the possible minimum and maximum lengths:
Minimum Length: x - 2.5 minutes
Maximum Length: x + 2.5 minutes
Therefore, the inequality that could be used to find the range lengths is:
x - 2.5 ≤ Actual Length ≤ x + 2.5
inequalities express a relationship between two quantities, indicating that one is greater than, less than, or not equal to the other. Symbolized by < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to), inequalities help compare values and represent ranges of possible solutions. Solving inequalities involves finding the valid intervals for the variable that satisfy the conditions. Inequalities are fundamental in algebra, calculus, and real-world problem-solving, providing a versatile tool for expressing relationships between values in a concise and mathematical manner.