The inequality `|1.5C-24|le30` represents the range of monthly average temperature, C, in degrees Celsius, during the winter month for a certain city. What was the lowest monthly average temperature, in degrees Celsius, for for this city?

Options

A. `-4`
B. `0`
C. `6`
D. `9`

Answer

To solve the inequality \( |1.5C - 24| \leq 30 \) and find the lowest monthly average temperature \( C \) in degrees Celsius for the city, we will follow these steps:

### Step 1: Break down the absolute value inequality
The inequality \( |1.5C - 24| \leq 30 \) can be rewritten as two separate inequalities:
\[ -30 \leq 1.5C - 24 \leq 30 \]

### Step 2: Solve the left part of the inequality
First, we solve the left part:
\[ 1.5C - 24 \geq -30 \]
Adding 24 to both sides:
\[ 1.5C \geq -30 + 24 \]
\[ 1.5C \geq -6 \]
Now, divide both sides by 1.5:
\[ C \geq \frac{-6}{1.5} \]
Calculating the right side:
\[ C \geq -4 \]

### Step 3: Solve the right part of the inequality
Now, we solve the right part:
\[ 1.5C - 24 \leq 30 \]
Adding 24 to both sides:
\[ 1.5C \leq 30 + 24 \]
\[ 1.5C \leq 54 \]
Now, divide both sides by 1.5:
\[ C \leq \frac{54}{1.5} \]
Calculating the right side:
\[ C \leq 36 \]

### Step 4: Combine the results
From the two parts, we have:
\[ -4 \leq C \leq 36 \]

### Conclusion
The lowest monthly average temperature \( C \) for the city is:
\[ \boxed{-4} \]