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. Distribute the -3 across the terms inside the parentheses: -3(x + 4) becomes -3x - 12.
2. Rewrite the equation with the distributed terms: 5x + 17 = 8x + 12 - 3x - 12.
3. Combine like terms on the right side of the equation. Combine 8x and -3x to get 5x, and combine 12 and -12 to get 0. The equation now is 5x + 17 = 5x.
4. Subtract 5x from both sides of the equation to isolate the constant terms: 5x + 17 - 5x = 5x - 5x, which simplifies to 17 = 0.
5. Since 17 = 0 is a false statement, the equation has no solution. Therefore, it is classified as an inconsistent equation.