Question
What is the undefined value for the equation
14= 7x/9/+4x
X≠-4//9
X≠9/4
X≠-9/4
X≠0
14= 7x/9/+4x
X≠-4//9
X≠9/4
X≠-9/4
X≠0
Answers
GPT-4o mini
To solve for the undefined value in the equation \( 14 = \frac{7x}{9} + 4x \), we first need to simplify the equation.
1. Combine terms on the right side:
\[
14 = \frac{7x}{9} + \frac{36x}{9} = \frac{7x + 36x}{9} = \frac{43x}{9}
\]
2. Now, we can write the equation as:
\[
14 = \frac{43x}{9}
\]
3. To eliminate the fraction, multiply both sides by 9:
\[
126 = 43x
\]
4. Now, solve for \( x \):
\[
x = \frac{126}{43}
\]
Next, we will analyze any restrictions or undefined values from the original equation. The only potential undefined values come from denominators:
In the original equation:
- \(\frac{7x}{9}\) does not create undefined values since the denominator is a constant (9).
- The term \(4x\) does not have any denominators that could lead to undefined behavior.
Thus, \( x \) can take any real value without resulting in undefined scenarios arising from the terms in the equation.
Therefore, the correct answer is that there are no undefined values in terms of restrictions on \( x \). However, if you are looking specifically at the options you've provided and assuming they refer to potentially undefined conditions, it's important to highlight that none of these options actually represent undefined values for the equation as given.
Based on the context of your question, if \( x \) were wrapped into a different form that causes division by zero, the undefined values could be valid. However, for this specific equation, \( x \) has no restrictions based on the terms provided.
1. Combine terms on the right side:
\[
14 = \frac{7x}{9} + \frac{36x}{9} = \frac{7x + 36x}{9} = \frac{43x}{9}
\]
2. Now, we can write the equation as:
\[
14 = \frac{43x}{9}
\]
3. To eliminate the fraction, multiply both sides by 9:
\[
126 = 43x
\]
4. Now, solve for \( x \):
\[
x = \frac{126}{43}
\]
Next, we will analyze any restrictions or undefined values from the original equation. The only potential undefined values come from denominators:
In the original equation:
- \(\frac{7x}{9}\) does not create undefined values since the denominator is a constant (9).
- The term \(4x\) does not have any denominators that could lead to undefined behavior.
Thus, \( x \) can take any real value without resulting in undefined scenarios arising from the terms in the equation.
Therefore, the correct answer is that there are no undefined values in terms of restrictions on \( x \). However, if you are looking specifically at the options you've provided and assuming they refer to potentially undefined conditions, it's important to highlight that none of these options actually represent undefined values for the equation as given.
Based on the context of your question, if \( x \) were wrapped into a different form that causes division by zero, the undefined values could be valid. However, for this specific equation, \( x \) has no restrictions based on the terms provided.