Question

What is the undefined value for the equation 14=7x9+4x ?(1 point)
Responses

x≠0
x does not equal 0

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

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

x≠−49

Answer 1

To determine the undefined value for the equation \(14 = 7 \times 9 + 4x\), we first need to solve for \(x\).

Rearranging the equation, we have:

1. Calculate \(7 \times 9\):
\[
7 \times 9 = 63
\]

2. Substitute into the equation:
\[
14 = 63 + 4x
\]

3. To isolate \(4x\), subtract \(63\) from both sides:
\[
14 - 63 = 4x
\]
\[
-49 = 4x
\]

4. Solve for \(x\) by dividing both sides by \(4\):
\[
x = \frac{-49}{4}
\]

This step shows that the value of \(x\) can be defined as \(-\frac{49}{4}\).

However, the question is about the undefined value, which typically means values that would make a denominator zero. In this case, we simply need to identify potential values that cannot be used if they were to be placed in a denominator in such an equation.

Given your options:

- \(x \neq 0\)
- \(x \neq -\frac{9}{4}\)
- \(x \neq \frac{9}{4}\)
- \(x \neq -49\)

None relate directly to the equation. Since there are no restrictions in the equation that lead to undefined values (like division by zero), we find that the option which states an equation has produced a valid result indicates the undefined situation.

The value that would make the equation undefined, although not explicitly listed in the mathematical process above, typically relates to complimentary angles (such as \(\frac{-49}{4}\) or \( \pm \text{some other factor} \)). In mathematical expressions dealing with fractions or variable denominators, typically the most basic exclusion is zero.

Among the available choices, the most relevant from a general standpoint (though not tied directly to the equation given it had no denominators initially) is:

- **\(x \neq -49\)** is simply stating values that could lead to diverging outputs in a different relevant expression situation.

Thus, the correct choice indicating exclusion for undefined behavior relevant to broader mathematical principles would be:
- **\(x \neq -49\)**.