If `-1leale4 and -6leble-2`, what is the minimum value for `b-a`?

Answer

To find the minimum value of \( b - a \) given the constraints \( -1 \leq a \leq 4 \) and \( -6 \leq b \leq -2 \), we can follow these steps:

### Step 1: Identify the ranges of \( a \) and \( b \)
From the problem, we have:
- For \( a \): \( -1 \leq a \leq 4 \)
- For \( b \): \( -6 \leq b \leq -2 \)

### Step 2: Determine the maximum value of \( a \)
The maximum value of \( a \) within its range is:
\[ a_{\text{max}} = 4 \]

### Step 3: Determine the minimum value of \( b \)
The minimum value of \( b \) within its range is:
\[ b_{\text{min}} = -6 \]

### Step 4: Substitute the values into the expression \( b - a \)
To find the minimum value of \( b - a \), we substitute the maximum value of \( a \) and the minimum value of \( b \):
\[ b - a = b_{\text{min}} - a_{\text{max}} = -6 - 4 \]

### Step 5: Calculate the result
Now, we perform the calculation:
\[ b - a = -6 - 4 = -10 \]

### Conclusion
Thus, the minimum value of \( b - a \) is:
\[ \boxed{-10} \]

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