The temperature at noon in Los Angeles on a summer day was 88°F. During the day the temperature varied from this by this much as 7.5°F. Write and solve an absolute value inequality to find the range of possible temperatures for that day?
|T-88| <= 7.5
88-7.5 <= T <= 88+7.5
...
To find the range of possible temperatures for the day, we need to consider the given temperature at noon (88°F) and the amount by which the temperature can vary (7.5°F).
Let's call the possible temperature values "x". The variations can be positive or negative, so we need to use absolute value notation. The absolute difference between "x" and the given temperature (88°F) should be less than or equal to the amount by which it can vary (7.5°F).
In inequality form, this can be expressed as:
| x - 88 | ≤ 7.5
To solve this inequality, we'll consider two cases: one where (x - 88) is positive, and one where it's negative.
Case 1: x - 88 ≥ 0
In this case, the absolute value is simply x - 88. So, we have:
x - 88 ≤ 7.5
Solving this inequality, we add 88 to both sides:
x ≤ 95.5
Case 2: x - 88 < 0
In this case, the absolute value becomes -(x - 88). So, we have:
-(x - 88) ≤ 7.5
Multiplying both sides by -1 reverses the inequality:
x - 88 ≥ -7.5
Adding 88 to both sides, we get:
x ≥ 80.5
By combining both cases, we find that the possible range of temperatures (in Fahrenheit) for the day is:
80.5 ≤ x ≤ 95.5
Therefore, the range of possible temperatures for that day in Los Angeles is between 80.5°F and 95.5°F.