Final answer:
The simplified equation 4(x + 3) - 4 = 8x + 10 - 4x results in the statement 8 = 10 after cancellation of variables, indicating there is no solution. It is an example of an inconsistent equation.
Step-by-step explanation:
The equation given is 4(x + 3) - 4 = 8x + 10 - 4x.
To solve this equation, we need to simplify and solve for x. Start by distributing 4 into the parentheses: 4x + 12 - 4 = 8x + 10 - 4x. Next, combine like terms: 4x + 8 = 4x + 10. Now, we subtract 4x from both sides to isolate the variable x, which gives us 8 = 10, which is not true, indicating that there is no solution to the equation since the variable x cancels out and results in an incorrect statement.
This type of equation is an example of an inconsistent equation.