Solve for u. 2/3 u = 1/2 + 5/3 u + 5/2 u – 2 u =

To solve for ( u ) in the equation:

[

frac{2}{3} u = frac{1}{2} + frac{5}{3} u + frac{5}{2} u – 2

]

First, let’s simplify the right side:

1. Combine the terms involving ( u ):

[

frac{5}{3} u + frac{5}{2} u

]

To combine these, we need a common denominator (which is 6):

[

frac{5}{3} u = frac{10}{6} u quad text{and} quad frac{5}{2} u = frac{15}{6} u

]

So,

[

frac{10}{6} u + frac{15}{6} u = frac{25}{6} u

]

2. Now, substitute back into the equation:

[

frac{2}{3} u = frac{1}{2} + frac{25}{6} u – 2

]

3. Convert ( frac{1}{2} ) and ( -2 ) to have a common denominator of 6:

[

frac{1}{2} = frac{3}{6} quad text{and}