Final answer:
Option C (40 + 7 = 30 + 7) is the linear equation that has no solution since it simplifies to the contradiction 47 = 37.
Step-by-step explanation:
The linear equation that has no solution is one that simplifies to a statement that is never true, such as a contradiction like 0 = 7. When solving linear equations like these, we aim to isolate the variable on one side and simplify the equation as much as possible to determine if it has a solution, no solution, or infinitely many solutions.
Let's analyze each given option:
A) 9x + 6 = 6x + 4 can be simplified to 3x + 6 = 4, further simplifying to 3x = -2. This equation has a solution when x = -2/3.
B) 5x + 12 = 5.2 - 7 simplifies to 5x + 12 = -1.8, which also has a solution after further simplification.
C) 40 + 7 = 30 + 7 simplifies to 47 = 37, which is a contradiction and indicates that this equation has no solution.
D) -3(2x - 5) = 15 - 6.0 simplifies to -6x + 15 = 15. This can be further reduced to -6x = 0, which has a solution x = 0.
Hence, the equation that has no solution is Option C.