a) To solve the equation |x - 7| + x - 7 = 0, we can split it into two cases:

Case 1: x - 7 ≥ 0
In this case, the absolute value |x - 7| is equal to x - 7. Therefore, the equation becomes (x - 7) + x - 7 = 0.
Simplifying this equation, we get 2x - 14 = 0.
Solving for x, we have 2x = 14, so x = 7.

Case 2: x - 7 < 0
In this case, the absolute value |x - 7| is equal to -(x - 7), which simplifies to -x + 7. Therefore, the equation becomes -x + 7 + x - 7 = 0.
Simplifying this equation, we get 0 = 0.
This equation is true for all values of x.

Therefore, the solution to the equation |x - 7| + x - 7 = 0 is x = 7.

b) To solve the equation 17 - x + |x - 4| = 0, we can split it into two cases:

Case 1: x - 4 ≥ 0
In this case, the absolute value |x - 4| is equal to x - 4. Therefore, the equation becomes 17 - x + (x - 4) = 0.
Simplifying this equation, we get 13 = 0.
This equation is not true, so there are no solutions in this case.

Case 2: x - 4 < 0
In this case, the absolute value |x - 4| is equal to -(x - 4), which simplifies to -x + 4. Therefore, the equation becomes 17 - x + (-x + 4) = 0.
Simplifying this equation, we get 21 - 2x = 0.
Solving for x, we have 2x = 21, so x = 10.5.

Therefore, the solution to the equation 17 - x + |x - 4| = 0 is x = 10.5.

c) To solve the equation |x - 3| + x - 3 = 0, we can split it into two cases:

Case 1: x - 3 ≥ 0
In this case, the absolute value |x - 3| is equal to x - 3. Therefore, the equation becomes (x - 3) + x - 3 = 0.
Simplifying this equation, we get 2x - 6 = 0.
Solving for x, we have 2x = 6, so x = 3.

Case 2: x - 3 < 0
In this case, the absolute value |x - 3| is equal to -(x - 3), which simplifies to -x + 3. Therefore, the equation becomes -x + 3 + x - 3 = 0.
Simplifying this equation, we get 0 = 0.
This equation is true for all values of x.

Therefore, the solution to the equation |x - 3| + x - 3 = 0 is x = 3.