Determine whether the equation is an identity, a conditional equation, or a contradiction. \[ 5(x+4)-19=5 x+1 \] This is an identity. This is a conditional equation. This is a contradiction.

To determine the nature of the equation \( 5(x+4)-19=5x+1 \), let's simplify it step by step. First, distribute on the left side: \[ 5x + 20 - 19 = 5x + 1 \] This simplifies to: \[ 5x + 1 = 5x + 1 \] Now, if we subtract \( 5x \) from both sides, we get: \[ 1 = 1 \] Since both sides are equal and true for all values of \( x \), this equation is indeed an identity. Furthermore, identifying equations like this can help strengthen your skills in algebra. When working with algebraic expressions, remember that the goal is to isolate variables and simplify appropriately. It’s easy to lose sight of the goal, but checking each step can help avoid common mistakes.