Solve.
5/3 x + 1/3 x = 7 + 7/3 x
The value of x is __.
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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 )