If `2a - 9 = b + a`, then the value of `(|a - b| + |b - a|)` is :

Options

A. 18
B. 11
C. 1
D. `0`

Answer

To solve the equation \( 2a - 9 = b + a \) and find the value of \( |a - b| + |b - a| \), we can follow these steps:

### Step 1: Rearranging the equation
We start with the equation:
\[ 2a - 9 = b + a \]
We can rearrange this to isolate \( b \):
\[ 2a - a - 9 = b \]
This simplifies to:
\[ a - 9 = b \]

### Step 2: Finding \( a - b \)
Now, we can find \( a - b \):
\[ a - b = a - (a - 9) \]
This simplifies to:
\[ a - b = a - a + 9 = 9 \]

### Step 3: Finding \( b - a \)
Next, we find \( b - a \):
\[ b - a = (a - 9) - a \]
This simplifies to:
\[ b - a = a - 9 - a = -9 \]

### Step 4: Calculating the absolute values
Now we calculate the absolute values:
\[ |a - b| = |9| = 9 \]
\[ |b - a| = |-9| = 9 \]

### Step 5: Adding the absolute values
Finally, we add the two absolute values:
\[ |a - b| + |b - a| = 9 + 9 = 18 \]

### Conclusion
Thus, the value of \( |a - b| + |b - a| \) is:
\[ \boxed{18} \]