Final answer:
Equations A and C have the correct solutions, while Equations B and D do not.
Step-by-step explanation:
In order to determine which equations have the correct solutions, we need to solve each equation and compare the solutions to the given values.
Equation A: 3n + 7 = 16
Solving for n:
3n = 16 - 7
3n = 9
n = 3
The solution n = 3 matches the given value, so Equation A is correct.
Equation B: 11 = (2/3)x - 1
Solving for x:
(2/3)x = 11 + 1
(2/3)x = 12
x = (3/2) * 12
x = 18
The solution x = 18 does not match the given value, so Equation B is not correct.
Equation C: (x + 3)/(-6) = 2x
Solving for x:
(x + 3)/(-6) = 2x
Multiplying both sides by -6:
x + 3 = -12x
Combining like terms:
13x = -3
x = -3/13
The solution x = -3/13 matches the given value, so Equation C is correct.
Equation D: 20 - 2t = 1/2 + 28
Solving for t:
20 - 2t = 1/2 + 28
Combining like terms:
-2t = 1/2 + 28 - 20
-2t = 9.5
t = -4.75
The solution t = -4.75 does not match the given value, so Equation D is not correct.
Based on these calculations, the correct solutions are:
A) n = 3
C) x = -3/13