A46 inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is one inch more than six times the length of the first piece

X=piece 1
2x= piece 2
6x+1= piece 3

46" total= x + (2x) + (6x+1)
combine like terms
46=9x+1
subtract 1 from both sides
45= 9x
divide both sides by 9
5"= x

Substitute x=5" to find length of all pieces:
x= 5" piece 1
2x= 2(5)= 10" piece 2
6x+1= 6(5)+1= 31" piece 3

Check:
46" total = 5" + 10" + 31"
46"= 46"

Hope this helps! :)