How can i divide thirty-three into two groups so the ratio is four to seven?

Look at it this way:

-- Since the two groups have the ratio of 4 to 7, then the first group has 4 parts
and the other group has 7 parts.

-- If the first group has 4 parts and the other group has 7 parts, then they have
11 parts all together.

-- Those 11 parts are all parts of 33.  There must be  ( 33 / 11 ) = 3 items in each part.

Now you can go back to the groups . . .

-- The first group has 4 parts. 
With 3 items in each part, that's (4 x 3) = 12 items.

-- The other group has 7 parts.
With 3 items in each part, that's (7 x 3) = 21 items.

x = 9

Step-by-step explanation:

7x + 3x - 18 = 6(x + 3)

10x - 18 = 6(x + 3)                  Add like terms

10x - 18 = 6x + 18                   Distribute 6 to x and 3

4x - 18 = 18                             Subtract 6x to both sides

4x = 36                                  Add 18 to both sides

x = 9                                      Divide 4 to both sides