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