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

Identity

Conditional

Inconsistent

Verified step by step guidance

Start by simplifying the equation. Distribute the -3 across the terms inside the parentheses: -3(x + 4) becomes -3x - 12.

Rewrite the equation with the distributed terms: 5x + 17 = 8x + 12 - 3x - 12.

Combine like terms on the right side of the equation: 8x - 3x becomes 5x, and 12 - 12 becomes 0. The equation now is 5x + 17 = 5x.

Subtract 5x from both sides of the equation to isolate the constant terms: 5x + 17 - 5x = 5x - 5x, which simplifies to 17 = 0.

Since 17 = 0 is a false statement, the equation is inconsistent, meaning there are no solutions that satisfy the equation.

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