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≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠94
?(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≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠94
Answers
Answer
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 negative 9 over 4 End Fraction
x≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠94
?(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≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠94
Answered by
GPT-4o mini
To find the undefined value for the equation \( 14 = 7 \cdot 9 + 4x \), we first need to simplify the equation.
1. Calculate \( 7 \cdot 9 \):
\[
7 \cdot 9 = 63
\]
2. Substitute that back into the equation:
\[
14 = 63 + 4x
\]
3. Now, isolate \( 4x \):
\[
4x = 14 - 63
\]
\[
4x = -49
\]
4. Divide by 4 to solve for \( x \):
\[
x = \frac{-49}{4}
\]
Now we analyze the potential choices for the undefined value:
1. \( x \neq 0 \)
2. \( x \neq -\frac{9}{4} \)
3. \( x \neq -\frac{49}{4} \) (which matches our solution)
4. \( x \neq 94 \)
Since we found that \( x = -\frac{49}{4} \), the correct response indicating the undefined value is:
**x ≠ -\(\frac{49}{4}\)** or **x does not equal -\(\frac{49}{4}\)**.
1. Calculate \( 7 \cdot 9 \):
\[
7 \cdot 9 = 63
\]
2. Substitute that back into the equation:
\[
14 = 63 + 4x
\]
3. Now, isolate \( 4x \):
\[
4x = 14 - 63
\]
\[
4x = -49
\]
4. Divide by 4 to solve for \( x \):
\[
x = \frac{-49}{4}
\]
Now we analyze the potential choices for the undefined value:
1. \( x \neq 0 \)
2. \( x \neq -\frac{9}{4} \)
3. \( x \neq -\frac{49}{4} \) (which matches our solution)
4. \( x \neq 94 \)
Since we found that \( x = -\frac{49}{4} \), the correct response indicating the undefined value is:
**x ≠ -\(\frac{49}{4}\)** or **x does not equal -\(\frac{49}{4}\)**.
Answered by
GPT-4o mini
To find the undefined value for the equation \( 14 = \frac{7x}{9} + 4x \), we need to solve for \( x \) and identify any values that would make the equation undefined.
1. First, rewrite the equation:
\[
14 = \frac{7x}{9} + 4x
\]
2. To eliminate the fraction, multiply every term by 9:
\[
14 \cdot 9 = 7x + 36x
\]
\[
126 = 43x
\]
3. Now solve for \( x \):
\[
x = \frac{126}{43}
\]
Next, we need to determine if any values make the expression undefined. The only potential issue in the original equation is when the denominator is zero. Since the equation contains \( \frac{7x}{9} \), the denominator is already a constant (9), which means it will never be zero.
Thus, the equation does not have any undefined points related to this denominator. However, \( x \) cannot take on any values at which \( 4x \) or \( \frac{7x}{9} \) yields division by zero, but since there are no such values in this equation, we can check the given options:
The responses provided are:
1. \( x \neq 0 \)
2. \( x \neq -\frac{9}{4} \)
3. \( x \neq -\frac{49}{4} \)
4. \( x \neq 94 \)
Among these options, **the only value that we must explicitly avoid to keep the equation meaningful is** \( x \neq 0 \). This empirically means that if \( x = 0 \), then both terms on the right side yield \( 0 \), leading to \( 14 \neq 0\), which is not true.
Therefore, the most relevant choice indicating the undefined behavior is:
**x ≠ 0**.
1. First, rewrite the equation:
\[
14 = \frac{7x}{9} + 4x
\]
2. To eliminate the fraction, multiply every term by 9:
\[
14 \cdot 9 = 7x + 36x
\]
\[
126 = 43x
\]
3. Now solve for \( x \):
\[
x = \frac{126}{43}
\]
Next, we need to determine if any values make the expression undefined. The only potential issue in the original equation is when the denominator is zero. Since the equation contains \( \frac{7x}{9} \), the denominator is already a constant (9), which means it will never be zero.
Thus, the equation does not have any undefined points related to this denominator. However, \( x \) cannot take on any values at which \( 4x \) or \( \frac{7x}{9} \) yields division by zero, but since there are no such values in this equation, we can check the given options:
The responses provided are:
1. \( x \neq 0 \)
2. \( x \neq -\frac{9}{4} \)
3. \( x \neq -\frac{49}{4} \)
4. \( x \neq 94 \)
Among these options, **the only value that we must explicitly avoid to keep the equation meaningful is** \( x \neq 0 \). This empirically means that if \( x = 0 \), then both terms on the right side yield \( 0 \), leading to \( 14 \neq 0\), which is not true.
Therefore, the most relevant choice indicating the undefined behavior is:
**x ≠ 0**.
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