The value of x is __.

To solve the equation ( frac{5}{3} x + frac{1}{3} x = 7 + frac{7}{3} x ), we can start by combining like terms on the left side.

1. Combine ( frac{5}{3} x ) and ( frac{1}{3} x ):

( frac{5}{3} x + frac{1}{3} x = frac{6}{3} x = 2 x )

2. Now the equation looks like this:

( 2x = 7 + frac{7}{3} x )

3. To eliminate the fraction on the right side, you can isolate ( x ):

First, let’s get all the ( x ) terms on one side:

( 2x – frac{7}{3} x = 7 )

4. Convert ( 2x ) into a fraction:

( 2x = frac{6}{3} x ), so now we have:

( frac{6}{3} x – frac{7}{3} x = 7 )

5. Combine the ( x ) terms:

( frac{-1}{3} x = 7 )

6. To solve for ( x ), multiply both sides by -3:

( x = 7 times -3 )