Question
what is undefined value for the equation 14 = 7x/9+4x
a. x ≠ -4/9
b. x ≠ -9/4
c. x ≠ 9/4
d. x ≠ 0
a. x ≠ -4/9
b. x ≠ -9/4
c. x ≠ 9/4
d. x ≠ 0
Answers
Answered by
GPT-4o mini
To find for which values of \( x \) the equation \( 14 = \frac{7x}{9} + 4x \) is undefined, we start by analyzing the equation.
1. Rearranging it:
\[
14 = \frac{7x}{9} + 4x
\]
2. Combine the terms on the right side, noticing that \( 4x = \frac{36x}{9} \):
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
This simplifies to:
\[
14 = \frac{43x}{9}
\]
3. To isolate \( x \), multiply both sides by \( 9 \):
\[
126 = 43x
\]
4. Then, divide by \( 43 \):
\[
x = \frac{126}{43}
\]
Now, we should check if there are any values that make the original equation undefined. In this case, the only potential source of an undefined value would be if we have a denominator equal to zero.
However, in the expression \( \frac{7x}{9} \), the denominator (which is 9) is a constant and cannot be zero. So it is never undefined.
Thus, none of the provided options correctly represent any value that would make the equation undefined since there are no values of \( x \) that lead to the equation being undefined.
The correct conclusion is that the given equation has no undefined value. So the answer could be phrased as:
None of the provided options (a, b, c, d) are correct since the equation is defined for all real numbers \( x \).
1. Rearranging it:
\[
14 = \frac{7x}{9} + 4x
\]
2. Combine the terms on the right side, noticing that \( 4x = \frac{36x}{9} \):
\[
14 = \frac{7x}{9} + \frac{36x}{9}
\]
This simplifies to:
\[
14 = \frac{43x}{9}
\]
3. To isolate \( x \), multiply both sides by \( 9 \):
\[
126 = 43x
\]
4. Then, divide by \( 43 \):
\[
x = \frac{126}{43}
\]
Now, we should check if there are any values that make the original equation undefined. In this case, the only potential source of an undefined value would be if we have a denominator equal to zero.
However, in the expression \( \frac{7x}{9} \), the denominator (which is 9) is a constant and cannot be zero. So it is never undefined.
Thus, none of the provided options correctly represent any value that would make the equation undefined since there are no values of \( x \) that lead to the equation being undefined.
The correct conclusion is that the given equation has no undefined value. So the answer could be phrased as:
None of the provided options (a, b, c, d) are correct since the equation is defined for all real numbers \( x \).
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