To determine the value of \( x \) that causes the rational equation \( 3x + 5 = 1x + 5 + 4 \) to be undefined, we first simplify the equation:
- Combine like terms on the right side: \[ 1x + 5 + 4 = 1x + 9 \] So the equation now reads: \[ 3x + 5 = 1x + 9 \]
Next, we can rearrange this equation to isolate \( x \):
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Subtract \( 1x \) from both sides: \[ 3x - 1x + 5 = 9 \implies 2x + 5 = 9 \]
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Next, subtract 5 from both sides: \[ 2x = 9 - 5 \implies 2x = 4 \]
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Now, divide both sides by 2 to solve for \( x \): \[ x = \frac{4}{2} \implies x = 2 \]
The question asks for the value of \( x \) that causes the rational equation to be undefined. Since this equation does not contain any rational expressions (divisions by \( x \) or similar that would cause undefined behavior), it is defined for all \( x \).
Therefore, there is no value of \( x \) that causes this equation to be undefined. The rational equation is valid for all \( x \).
Hence, the answer is: There is no value of \( x \) that causes the equation to be undefined.