A32-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third is 4 times as long as the first piece. if x represents the length of the first piece, find the lengths of all three pieces

If x is the length of the first piece, then the 2nd is 3x and the 3rd is 4x.
the length of the board is 32 inches so
32=x + 3x + 4x
32= 8x (add all like values)
32/8=(8x)/8 (divide both sides by 8
4=x
first piece is 4 inches
second piece is 3x so 3(4)=12 inches
third piece is 4x so 4(4)=16 inches