To determine when the equation \( 3x + 5 = 1x + 5 + 4 \) is undefined, we first simplify the equation:
\[ 1x + 5 + 4 = 1x + 9 \]
So, we rewrite the equation as:
\[ 3x + 5 = 1x + 9 \]
Next, we can rearrange the equation by bringing like terms together:
\[ 3x - 1x = 9 - 5 \]
This simplifies to:
\[ 2x = 4 \]
Dividing both sides by 2 gives us:
\[ x = 2 \]
However, the question asks for values of \( x \) that cause the equation to be undefined. A rational equation is typically undefined when there is a division by zero. Since \( 3x + 5 \) and \( 1x + 9 \) do not involve any denominators in this equation, it is defined for all values of \( x \).
Thus, there is no value of \( x \) that causes this rational equation to be undefined. The original form of the equation does not present any divisions that could lead to undefined situations.