Question
What is the undefined value for the equation 14 =7x/9+4x
?(1 point)
Responses
x ≠ −4/9
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠ 9/4
x does not equal Start Fraction 9 over 4 End Fraction
x ≠−9/4
x does not equal Start Fraction negative 9 over 4 End Fraction
x ≠ 0
?(1 point)
Responses
x ≠ −4/9
x does not equal Start Fraction negative 4 over 9 End Fraction
x≠ 9/4
x does not equal Start Fraction 9 over 4 End Fraction
x ≠−9/4
x does not equal Start Fraction negative 9 over 4 End Fraction
x ≠ 0
Answers
GPT-4o mini
To determine if there are any undefined values for the equation \( 14 = \frac{7x}{9} + 4x \), let's first solve the equation for \( x \).
Start by combining the terms on the right side:
\[
14 = \frac{7x}{9} + 4x
\]
Convert \( 4x \) into a fraction with a denominator of 9:
\[
4x = \frac{36x}{9}
\]
Now substitute this back into the equation:
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
Combine the fractions:
\[
14 = \frac{7x + 36x}{9}
\]
\[
14 = \frac{43x}{9}
\]
To eliminate the fraction, multiply both sides by 9:
\[
14 \cdot 9 = 43x
\]
\[
126 = 43x
\]
Now solve for \( x \):
\[
x = \frac{126}{43}
\]
Since the equation can be solved and does not involve any radical expressions or divisions by zero, there are no undefined values for \( x \).
None of the provided answer choices correspond to any exclusion values. Since the equation is defined for all real values of \( x \) and we obtained \( x = \frac{126}{43} \) with no restrictions, the answer is not listed among the options. If you are specifically looking for restrictions, there are none for this equation.
Given your options, they don't apply in this scenario. However, if considering the context, the correct implication here would be that there are no undefined values for \( x \) in this equation.
Start by combining the terms on the right side:
\[
14 = \frac{7x}{9} + 4x
\]
Convert \( 4x \) into a fraction with a denominator of 9:
\[
4x = \frac{36x}{9}
\]
Now substitute this back into the equation:
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
Combine the fractions:
\[
14 = \frac{7x + 36x}{9}
\]
\[
14 = \frac{43x}{9}
\]
To eliminate the fraction, multiply both sides by 9:
\[
14 \cdot 9 = 43x
\]
\[
126 = 43x
\]
Now solve for \( x \):
\[
x = \frac{126}{43}
\]
Since the equation can be solved and does not involve any radical expressions or divisions by zero, there are no undefined values for \( x \).
None of the provided answer choices correspond to any exclusion values. Since the equation is defined for all real values of \( x \) and we obtained \( x = \frac{126}{43} \) with no restrictions, the answer is not listed among the options. If you are specifically looking for restrictions, there are none for this equation.
Given your options, they don't apply in this scenario. However, if considering the context, the correct implication here would be that there are no undefined values for \( x \) in this equation.
can 126/43 be divided into a smaller number to become of the provided answers?
GPT-4o mini
Let's simplify \( \frac{126}{43} \) and see if it can relate to any of the provided choices.
First, we can perform the division:
- \( 126 \div 43 \) does not yield any integer, but we can find the decimal representation if necessary.
Calculating it gives approximately:
\[
126 \div 43 \approx 2.9302
\]
Now let's examine the responses provided:
1. \( x \neq -\frac{4}{9} \)
2. \( x \neq \frac{9}{4} \)
3. \( x \neq -\frac{9}{4} \)
4. \( x \neq 0 \)
None of these options can be derived from \( \frac{126}{43} \). To check if \( \frac{126}{43} \) is equivalent to any of these options, we can also convert the fractions to decimal form:
- \( -\frac{4}{9} \approx -0.4444 \)
- \( \frac{9}{4} = 2.25 \)
- \( -\frac{9}{4} = -2.25 \)
- \( 0 = 0 \)
None of these values or their corresponding fractions match \( \frac{126}{43} \approx 2.9302 \).
In conclusion, \( \frac{126}{43} \) cannot be simplified or reduced to produce any of the options provided. Therefore, there are no restrictions on \( x \) for the original equation, and the given options do not apply.
First, we can perform the division:
- \( 126 \div 43 \) does not yield any integer, but we can find the decimal representation if necessary.
Calculating it gives approximately:
\[
126 \div 43 \approx 2.9302
\]
Now let's examine the responses provided:
1. \( x \neq -\frac{4}{9} \)
2. \( x \neq \frac{9}{4} \)
3. \( x \neq -\frac{9}{4} \)
4. \( x \neq 0 \)
None of these options can be derived from \( \frac{126}{43} \). To check if \( \frac{126}{43} \) is equivalent to any of these options, we can also convert the fractions to decimal form:
- \( -\frac{4}{9} \approx -0.4444 \)
- \( \frac{9}{4} = 2.25 \)
- \( -\frac{9}{4} = -2.25 \)
- \( 0 = 0 \)
None of these values or their corresponding fractions match \( \frac{126}{43} \approx 2.9302 \).
In conclusion, \( \frac{126}{43} \) cannot be simplified or reduced to produce any of the options provided. Therefore, there are no restrictions on \( x \) for the original equation, and the given options do not apply.