We can start solving this equation by isolating the absolute value expression on one side of the equation:
|2x+13| - 1 = 6
|2x+13| = 7
Next, we can split this equation into two separate cases, depending on whether 2x+13 is positive or negative. If it's positive, we can drop the absolute value bars, and if it's negative, we need to flip the sign inside the absolute value bars:
2x + 13 = 7 or -(2x + 13) = 7
Solving the first equation, we get:
2x = -6
x = -3
Solving the second equation, we get:
-2x - 13 = 7
-2x = 20
x = -10
Therefore, the solution set for the equation |2x+13|-1=6 is { -10 , -3 }.