Question

What value of x causes the rational equation 3x+5=1x+5+4
to be undefined?

Answer 1

To determine the value of \( x \) that causes the rational equation \( 3x + 5 = 1x + 5 + 4 \) to be undefined, we first simplify the equation:

1. 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 \( x \):

2. Subtract \( 1x \) from both sides:
\[
3x - 1x + 5 = 9 \implies 2x + 5 = 9
\]

3. Next, subtract 5 from both sides:
\[
2x = 9 - 5 \implies 2x = 4
\]

4. 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.**