What is the undefined value for the equation 14=7x/9+4x ?(1 point)

Question

Responses

x≠94
x does not equal Start Fraction 9 over 4 End Fraction

x≠−49
x does not equal Start Fraction negative 4 over 9 End Fraction

x≠0
x does not equal 0

x≠−94

Answer 1

To find the value of \( x \) that makes the equation \( 14 = \frac{7x}{9} + 4x \) undefined, we first need to manipulate the equation to isolate \( x \).

Let's rewrite the equation:

\[ 14 = \frac{7x}{9} + 4x \]

Next, we'll simplify by finding a common denominator for the terms on the right:

\[ 4x = \frac{36x}{9} \]

Now substituting this back into the equation gives:

\[ 14 = \frac{7x}{9} + \frac{36x}{9} \]

Combine the fractions:

\[ 14 = \frac{7x + 36x}{9} \]

This simplifies to:

\[ 14 = \frac{43x}{9} \]

Now, we can multiply both sides by 9 to eliminate the fraction:

\[ 14 \times 9 = 43x \]

\[ 126 = 43x \]

Now, divide both sides by 43:

\[ x = \frac{126}{43} \]

This value will not make the equation undefined, as it is simply a value for \( x \).

In rational expressions, they can become undefined when the denominator equals zero. However, in this equation, there are no denominators that depend on \( x \) that could potentially become zero, so the equation itself does not indicate any restrictions on \( x \).

Therefore, none of the suggested responses indicate an undefined value in this context. All options provided seem to reflect specific values of \( x \) rather than the absence of restrictions.

If the question was looking for which values would lead to the function being undefined, none would fit this scenario since this equation does not restrict \( x \) to make it undefined.

Thus, the correct conclusion is that there are no undefined values for this equation regarding \( x \).

Answer 2

incorrect

Answer 3

I apologize for any misunderstanding. Let's analyze the original equation again for any potential undefined values.

The equation given is:

\[ 14 = \frac{7x}{9} + 4x \]

To express this in a simpler form, let's focus on the right-hand side first:

\[ \frac{7x}{9} + 4x = \frac{7x}{9} + \frac{36x}{9} = \frac{7x + 36x}{9} = \frac{43x}{9} \]

Now, the equation becomes:

\[ 14 = \frac{43x}{9} \]

Next, we multiply both sides by 9 to eliminate the fraction:

\[ 14 \cdot 9 = 43x \]

This simplifies to:

\[ 126 = 43x \]

Now, solving for \( x \):

\[ x = \frac{126}{43} \]

This value does not lead to a division by zero, as there are no denominators in the expression that relate to \( x \) that could cause undefined behavior.

Looking for Undefined Values

The equation will only be undefined if there are values of \( x \) that result in a division by zero. In this equation, the only potential division occurs in \( \frac{7x}{9} \). The denominator (9) never equals zero regardless of the value of \( x \).

To generate undefined behavior in an expression, we typically look at scenarios where a denominator could be zero, which isn't present here because the fraction \( \frac{7x}{9} \) will never be undefined.

The options you provided suggest specific negative/positive fractions or integers that presumably are meant to cause confusion around undefined conditions. However, none of them stem from any restrictions provided by the equation.

If you meant there could be undefined conditions in a differently structured equation or a different fraction involving \( x \), please clarify any additional context.

Summary of Response

• From the closure performed on \( 14 = \frac{7x}{9} + 4x \), no values make the expression undefined as the denominator \( 9 \) does not include \( x \).
• Initial answers provided in terms of undefined values may refer to other equations, or further context on which part led to confusion may be needed.

If you could provide more clarity on the expectations for undefined values or on any follow-up conditions in a related question, I'd deduce a more accurate guiding response. Thank you for your understanding!