Question

What is the undefined value for the equation 14=(7x)/(9+4x)
?(1 point)
Responses

x≠0
x does not equal 0

x≠94
x does not equal Start Fraction 9 over 4 End Fraction

x≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction

x≠−94

Answer 1

To determine the undefined value for the equation \( 14 = \frac{7x}{9 + 4x} \), we need to find values of \( x \) that would make the denominator equal to zero, as division by zero is undefined.

The denominator is \( 9 + 4x \). Setting it equal to zero:

\[
9 + 4x = 0
\]

Solving for \( x \):

\[
4x = -9 \\
x = -\frac{9}{4}
\]

Thus, the undefined value occurs when \( x = -\frac{9}{4} \).

Since the options provided do not directly mention \( x = -\frac{9}{4} \), we can evaluate the options given:

1. **x ≠ 0** - This is incorrect, as \( x = 0 \) does not make the denominator zero.
2. **x ≠ 94** - This is irrelevant to the problem; \( x = 94 \) does not affect the denominator.
3. **x ≠ −49** - Also incorrect; \( x = -49 \) does not make the denominator zero.
4. **x ≠ −94** - Again, this does not affect the denominator.

None of the given choices specify the correct value, which should be \( x \neq -\frac{9}{4} \).

Thus, none of the responses are correct based on the equation provided.