Question
What is the undefined value for the equation 14= 7x/9+4x
?
(1 point)
Responses
x≠ −4/9
x≠ 9/4
x≠ −9/4
x≠0
?
(1 point)
Responses
x≠ −4/9
x≠ 9/4
x≠ −9/4
x≠0
Answers
Answered by
GPT-4o mini
To solve the equation \( 14 = \frac{7x}{9} + 4x \) and determine any undefined values, we first need to find the solution for \( x \).
1. Start by rewriting the equation:
\[
14 = \frac{7x}{9} + 4x
\]
2. To combine the terms on the right side, express \( 4x \) in terms of a common denominator (9):
\[
4x = \frac{36x}{9}
\]
3. Now substitute back:
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
\[
14 = \frac{7x + 36x}{9}
\]
\[
14 = \frac{43x}{9}
\]
4. Now, multiply both sides by 9 to eliminate the denominator:
\[
14 \cdot 9 = 43x
\]
\[
126 = 43x
\]
5. Now, solve for \( x \):
\[
x = \frac{126}{43}
\]
The question asks for undefined values. The expression \(\frac{7x}{9} + 4x\) does not introduce any denominators that might cause an undefined value (other than division by zero). Since there are no restrictions that would create undefined values in this equation, the only potential outcome is that this equation is defined for all real numbers except those values which do cause the operations to be undefined.
Thus, in this context, none of the options given really reflect what we derived. However, when we solve for \( x \), we did not find any values that make the equation undefined since \( x = \frac{126}{43} \) is a valid solution.
Therefore, based on the responses you provided, the correct answer is not among the options listed. If you're looking for exclusions based on the operation itself, all values \( x \) are valid here.
1. Start by rewriting the equation:
\[
14 = \frac{7x}{9} + 4x
\]
2. To combine the terms on the right side, express \( 4x \) in terms of a common denominator (9):
\[
4x = \frac{36x}{9}
\]
3. Now substitute back:
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
\[
14 = \frac{7x + 36x}{9}
\]
\[
14 = \frac{43x}{9}
\]
4. Now, multiply both sides by 9 to eliminate the denominator:
\[
14 \cdot 9 = 43x
\]
\[
126 = 43x
\]
5. Now, solve for \( x \):
\[
x = \frac{126}{43}
\]
The question asks for undefined values. The expression \(\frac{7x}{9} + 4x\) does not introduce any denominators that might cause an undefined value (other than division by zero). Since there are no restrictions that would create undefined values in this equation, the only potential outcome is that this equation is defined for all real numbers except those values which do cause the operations to be undefined.
Thus, in this context, none of the options given really reflect what we derived. However, when we solve for \( x \), we did not find any values that make the equation undefined since \( x = \frac{126}{43} \) is a valid solution.
Therefore, based on the responses you provided, the correct answer is not among the options listed. If you're looking for exclusions based on the operation itself, all values \( x \) are valid here.