Final answer:
The sum of the solutions to the equation |3x-7| = 5 is 14/3.
Step-by-step explanation:
The given equation |3x-7| = 5 represents an absolute value equation.
To find the sum of the solutions, we need to solve the equation for both cases when the expression inside the absolute value is positive and negative.
When 3x-7 is positive, we have 3x-7 = 5. Then :
3x = 5 + 7
3x = 12
x = 4.
When 3x-7 is negative, we have -(3x-7) = 5.
Simplifying this equation gives -3x+7 = 5. Then:
3x = 7 - 5
3x = 2
x = 2 / 3
Therefore, the sum of the solutions is 4+ 2/3 = 14/3.