The absolute value of the sum of the abscissas of all the points on the line `x+y=4` that lie at a unit distance from the line `4x+3y-10=0` is___________

Explanation

To solve the problem, we need to find the absolute value of the sum of the abscissas of all the points on the line \(x + y = 4\) that lie at a unit distance from the line \(4x + 3y - 10 = 0\).

### Step-by-Step Solution:

1. **Identify a point on the line \(x + y = 4\)**:
Let the point on the line be represented as \( (h, 4 - h) \).

2. **Calculate the distance from the point to the line \(4x + 3y - 10 = 0\)**:
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