1/2(6x-4)=4x-9

Please help me solve this and show your work please and thank you

multiply by 2 on both sides

6x-4=8x-18
then subtract 6x to the other side
-4=8x-6x-18
then add 18 to the other side
-4+18=8x-6x
and then simplify and then solve for x
14=2x
x=7