If `|x|le2 and |y|le1`, then what is the least possible value of x-y?

Options

A. `-3`
B. `-2`
C. `-1`
D. `0`

Answer

To find the least possible value of \( x - y \) given the constraints \( |x| \leq 2 \) and \( |y| \leq 1 \), we can follow these steps:

### Step 1: Determine the range of \( x \)
The condition \( |x| \leq 2 \) implies:
\[ -2 \leq x \leq 2 \]
This means that \( x \) can take any value from -2 to 2.

### Step 2: Determine the range of \( y \)
The condition \( |y| \leq 1 \) implies:
\[ -1 \leq y \leq 1 \]
This means that \( y \) can take any value from -1 to 1.

### Step 3: Find the least value of \( x - y \)
To minimize \( x - y \), we need to choose the smallest possible value for \( x \) and the largest possible value for \( y \):
- The minimum value of \( x \) is \( -2 \).
- The maximum value of \( y \) is \( 1 \).

Now, we can calculate \( x - y \):
\[ x - y = -2 - 1 = -3 \]

### Conclusion
Thus, the least possible value of \( x - y \) is:
\[ \boxed{-3} \]

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