The temperature, t, in degrees Fahrenheit, in a certain town on a certain spring day satisfies the inequality `|t - 24| le 30`. Which of the followig temperatures , in degrees Fahrenheit, is NOT in this range?

Options

A. `-10`
B. `-6`
C. `-5`
D. `0`

Answer

To solve the inequality \( |t - 24| \leq 30 \) and determine which temperature is NOT in the specified range, we can follow these steps:

### Step 1: Understand the inequality
The inequality \( |t - 24| \leq 30 \) means that the distance between \( t \) and 24 is at most 30 degrees.

### Step 2: Rewrite the absolute value inequality
We can break down the absolute value inequality into two separate inequalities:
\[ -30 \leq t - 24 \leq 30 \]

### Step 3: Solve the inequalities
Now we will solve the two inequalities separately.

1. **For the left side:**
\[ t - 24 \geq -30 \]
Adding 24 to both sides:
\[ t \geq -30 + 24 \]
\[ t \geq -6 \]

2. **For the right side:**
\[ t - 24 \leq 30 \]
Adding 24 to both sides:
\[ t \leq 30 + 24 \]
\[ t \leq 54 \]

### Step 4: Combine the results
From the two inequalities, we have:
\[ -6 \leq t \leq 54 \]
This means that the temperature \( t \) must be between -6 degrees Fahrenheit and 54 degrees Fahrenheit, inclusive.

### Step 5: Check the options
Now we need to check which of the given temperature options is NOT in the range \([-6, 54]\).

Assuming the options provided are:
- A) -10
- B) 0
- C) 30
- D) 55

We can evaluate each option:
- **Option A: -10** (Not in the range since -10 < -6)
- **Option B: 0** (In the range since -6 ≤ 0 ≤ 54)
- **Option C: 30** (In the range since -6 ≤ 30 ≤ 54)
- **Option D: 55** (Not in the range since 55 > 54)

### Conclusion
The temperature that is NOT in the range is **Option A: -10**.

---