The solution to the first equation is v = 1, and the correct statement is "V = 1".
The only solution to the equation is u = 1/3.
Let's analyze each equation to determine its solution and the corresponding statement:
Equation 1:
4(v + 2) + 2 = 2(v + 6)
Expanding the left side:
4v + 8 + 2 = 2v + 12
Combining like terms:
6v + 10 = 2v + 12
Subtracting 2v from both sides:
4v + 10 - 2v = 2v + 12 - 2v
2v + 10 = 12
Subtracting 10 from both sides:
2v + 10 - 10 = 12 - 10
2v = 2
Dividing both sides by 2:
2v/2 = 2/2
v = 1
Therefore, the solution to the first equation is v = 1, and the correct statement is "V = 1".
Equation 2:
3(2+u) u = 6 + 2(u + 1)
Expanding the left side:
6u + 3u^2 = 6 + 2u + 2
Combining like terms:
3u^2 + 4u - 4 = 0
Factoring the expression:
(u + 4)(3u - 1) = 0
Therefore, either u + 4 = 0 or 3u - 1 = 0. Solving for u in each case:
u + 4 = 0, so u = -4
3u - 1 = 0, so u = 1/3
However, the original equation is undefined when u = -4. Therefore, the only solution to the equation is u = 1/3, and the correct statement is "u = 1/3".