Question

What is the undefined value for the equation 14=7x/9+4x ?(1 point) Responses x≠0
x≠−9/4
x≠9/4
x≠−4 / 9

Answer 1

To determine the undefined values for the equation \( 14 = \frac{7x}{9} + 4x \), we first need to rearrange and solve the equation for \( x \).

1. Combine terms on the right side:
\[
4x = \frac{36x}{9} \quad \text{(since \( 4 \) can be written as \( \frac{36}{9} \))}
\]
Thus, we have:
\[
14 = \frac{7x + 36x}{9}
\]
Simplifying this, we get:
\[
14 = \frac{43x}{9}
\]

2. Multiply both sides by \( 9 \):
\[
14 \times 9 = 43x
\]
\[
126 = 43x
\]

3. Divide by \( 43 \):
\[
x = \frac{126}{43}
\]

Now, check if any values make the equation undefined. In this equation, the only potential for undefined occurs where there is division by zero.

The original equation is \( \frac{7x}{9} + 4x \) does not include any expressions that would result in division by zero. The fraction \( \frac{7x}{9} \) is only undefined if the denominator is zero, but here, \( 9 \) is always nonzero.

Since \( x \) does not make the fractions undefined in this equation, the only consideration could be around division by \( 0 \). However, since there are no horizontal asymptotes or denominators that could lead to undefined points based on this equation structure, there aren't any undefined values for \( x \) in this context.

So, the conclusion is that none of the provided responses apply, hence the problem likely has none of these stated undefined values related to the equation as presented.

If still refocusing on the responses, if defined to check for undefined values from a viewpoint of residual notation, the best approach as per conventional norms would state:

- **x ≠ -9/4**, **x ≠ +9/4**, **x ≠ -4/9**, and **x ≠ 0** are not applicable in this specific equation.

Thus, none of the stated conditions qualify against division by \( 0\).

This means that:
- The equation does not restrict any values of \( x\), and therefore, it does not have undefined values under the given conditions.