Answer:
C. 8(x-3) + 14 = 2(4x+5).
Explanation:
To determine which equation has no solutions, we need to solve each equation and check if there is a solution. Here's a step-by-step explanation:
A. 3(2x+7) = 6(x+4) - 3
Simplifying both sides:
6x + 21 = 6x + 24 - 3
6x + 21 = 6x + 21
Notice that the variable cancels out on both sides, resulting in a true statement. This equation has infinitely many solutions.
B. 3(6x-5) = 3(6x-5) + x
Simplifying both sides:
18x - 15 = 18x - 15 + x
18x - 15 = 18x - 15 + x
Again, the variable cancels out on both sides, resulting in a true statement. This equation also has infinitely many solutions.
C. 8(x-3) + 14 = 2(4x+5)
Simplifying both sides:
8x - 24 + 14 = 8x + 10
8x - 10 = 8x + 10
The variable cancels out on both sides, resulting in a false statement (-10 ≠ 10). This equation has no solutions.
D. 13x - 7 = 12(x-1) + x + 5
Simplifying both sides:
13x - 7 = 12x - 12 + x + 5
13x - 7 = 13x - 7
The variable cancels out on both sides, resulting in a true statement. This equation has infinitely many solutions.