Question
What is the undefined value for the equation 14 = 7x9 + 4x ?(1 point) Responses x≠−94 x is not equal to negative 9 over 4 x≠−49 x is not equal to negative 4 over 9 x≠94 x is not equal to 9 fourths x≠0
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Answered by
GPT-4o mini
To determine if there is an undefined value in the equation \( 14 = 7 \cdot 9 + 4x \), let's first simplify the equation.
Start by evaluating \( 7 \cdot 9 \):
\[
7 \cdot 9 = 63
\]
Now substitute this back into the equation:
\[
14 = 63 + 4x
\]
Next, isolate \( 4x \) by subtracting \( 63 \) from both sides:
\[
14 - 63 = 4x
\]
\[
-49 = 4x
\]
Now, divide both sides by \( 4 \):
\[
x = -\frac{49}{4}
\]
Since this is the only value for \( x \) derived from the equation, there are no undefined values in the context of \( x \) from this equation.
Thus, any of the response choices that indicate \( x \) cannot be a certain value might need to be reevaluated. The equation does not have any restrictions that lead to undefined values based on basic algebraic interpretation.
However, the closest option that suggests an invalid input to prevent zero denominators or other restrictions would be:
- \( x \neq -\frac{49}{4} \)
Since if \( 4x \) were to be equated to anything that could lead to division by zero, that would be of interest. Yet, since "undefined value" typically refers to a restriction due to a division by zero or similar situation, none of these responses are actually appropriate based on pure evaluation.
If we had to pick the closest relevant restriction:
**x ≠ −49** correlates to the derived value of \( x = -\frac{49}{4} \). The answer isn't listed explicitly, but interpreting the constraints, one could assume a misphrasing in the response options.
Ultimately, confirm the expected interpretations of undefined in the given context, but from what's derived, \( x \) has a finite solution with no explicit undefined markers. Thus none ultimately fit standard conventions of "undefined" in the presented form.
Start by evaluating \( 7 \cdot 9 \):
\[
7 \cdot 9 = 63
\]
Now substitute this back into the equation:
\[
14 = 63 + 4x
\]
Next, isolate \( 4x \) by subtracting \( 63 \) from both sides:
\[
14 - 63 = 4x
\]
\[
-49 = 4x
\]
Now, divide both sides by \( 4 \):
\[
x = -\frac{49}{4}
\]
Since this is the only value for \( x \) derived from the equation, there are no undefined values in the context of \( x \) from this equation.
Thus, any of the response choices that indicate \( x \) cannot be a certain value might need to be reevaluated. The equation does not have any restrictions that lead to undefined values based on basic algebraic interpretation.
However, the closest option that suggests an invalid input to prevent zero denominators or other restrictions would be:
- \( x \neq -\frac{49}{4} \)
Since if \( 4x \) were to be equated to anything that could lead to division by zero, that would be of interest. Yet, since "undefined value" typically refers to a restriction due to a division by zero or similar situation, none of these responses are actually appropriate based on pure evaluation.
If we had to pick the closest relevant restriction:
**x ≠ −49** correlates to the derived value of \( x = -\frac{49}{4} \). The answer isn't listed explicitly, but interpreting the constraints, one could assume a misphrasing in the response options.
Ultimately, confirm the expected interpretations of undefined in the given context, but from what's derived, \( x \) has a finite solution with no explicit undefined markers. Thus none ultimately fit standard conventions of "undefined" in the presented form.
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