Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. 
$5x+17=8x+12-3\left(x+4\right)$

• A. Identity
• B. Conditional
• C. Inconsistent

Answer: (C)

Verified step by step guidance

1. Start by simplifying the equation on both sides. Distribute the -3 on the right side: 5x + 17 = 8x + 12 - 3(x + 4).
2. Distribute -3 into (x + 4) to get: 5x + 17 = 8x + 12 - 3x - 12.
3. Combine like terms on the right side: 5x + 17 = (8x - 3x) + (12 - 12).
4. Simplify the right side: 5x + 17 = 5x + 0.
5. Subtract 5x from both sides to isolate the constant terms: 5x + 17 - 5x = 5x - 5x. This simplifies to 17 = 0, which is a contradiction, indicating the equation is inconsistent.