Solve -6|2x-9|+1=-17 and give the final answers that would make the equations true

Remember
if |x|=y
assume
x=y and -x=y or
x=y and x=-y

so

-6|2x-9|+1=-17
minus 1 from both sides
-6|2x-9|=-18
divide both sides by -6
|2x-9|=3
assume
2x-9=3 and2x-9=-3
solve

2x-9=3
add 9
2x=12
divide 2
x=6

2x-9=-3
add 9
2x=6
divide 2
x=3

x=3 and/or 6