What is the undefined value for the equation 14=7x9+4x ?(1 point) Responses x≠94 x does not equal Start Fraction 9 over 4 End Fraction x≠−94 x does not equal Start Fraction negative 9 over 4 End Fraction x≠−49 x does not equal Start Fraction negative 4 over 9 End Fraction x≠0

Question

GPT-4o mini · Answer

To solve the equation $ 14 = 7 \times 9 + 4x $ for $ x $: 1. First, calculate $ 7 \times 9 $: $$ 7 \times 9 = 63 $$ 2. Substitute that back into the equation: $$ 14 = 63 + 4x $$ 3. Now, isolate $ 4x $ by subtracting 63 from both sides: $$ 14 - 63 = 4x $$ $$ -49 = 4x $$ 4. Next, solve for $ x $ by dividing both sides by 4: $$ x = \frac{-49}{4} $$ The equation has defined a value for $ x $, which is $ \frac{-49}{4} $. Now let's check which of the choices indicates the undefined value for $ x $: - $ x \neq 94 $ - $ x \neq \frac{9}{4} $ - $ x \neq -94 $ - $ x \neq \frac{-9}{4} $ - $ x \neq -49 $ - $ x \neq \frac{-4}{9} $ - $ x \neq 0 $ None of these provide an undefined expression related to the derived value of $ x = \frac{-49}{4} $. Generally, undefined values in equations occur when a division by zero occurs. In this case, however, none of the responses indicate a division by zero or other mathematical condition that negates $ x $. Hence, if you were looking for valid conditions to avoid, the correct answer is $ x \neq \frac{-49}{4} $. As none of the options match, the correct selection essentially should signify avoiding the derived solution rather than presenting an undefined state or a condition that leads to a problem within the context of the presented equation. If the answer should reflect the calculated state: If considering the answer in terms of avoidance of undefined values specifically focused on divisions and restrictions applied to $ x $, the responses provided do not contain issues indicating $ x = \frac{-49}{4} $ as undefined within communal limits. To summarize: If just considering how to avoid specific results, $ x \neq \frac{-49}{4} $ should be reflected there if desired mention of value relating to equality displays required marking upon fulfillments directly answering the query accordingly towards clarity via placement structure defined within real-number arc.

Honeybeee · Answer

What is the undefined value for the equation 14=7x/9+4x ?(1 point) Responses x≠94 x does not equal Start Fraction 9 over 4 End Fraction x≠−94 x does not equal Start Fraction negative 9 over 4 End Fraction x≠−49 x does not equal Start Fraction negative 4 over 9 End Fraction x≠0

GPT-4o mini · Answer

To find the undefined value for the equation $ 14 = \frac{7x}{9} + 4x $, let's analyze it step by step.

Rearranging the equation gives: \[ 14 = \frac{7x}{9} + 4x \]
To combine the terms, let's express $ 4x $ with a common denominator of 9: \[ 4x = \frac{36x}{9} \] Therefore, we can rewrite the equation as: \[ 14 = \frac{7x + 36x}{9} \] Which simplifies to: \[ 14 = \frac{43x}{9} \]
Now, multiply both sides by 9 to eliminate the fraction: \[ 14 \times 9 = 43x \] \[ 126 = 43x \]
Finally, solve for $ x $: \[ x = \frac{126}{43} \]

None of these steps indicate a division by zero, which is typically where we encounter undefined values related to $ x $.

However, in exploring the constraints for the variable, we notice potential restrictions in terms of what $ x $ could equal. The original equation's denominator (the $ 9 $ in $ \frac{7x}{9} $) does not lead to restrictions based on typical operations.

Looking at the responses provided:

$ x \neq 94 $
$ x \neq \frac{9}{4} $
$ x \neq -94 $
$ x \neq \frac{-9}{4} $
$ x \neq -49 $
$ x \neq \frac{-4}{9} $
$ x \neq 0 $

The undefined values would likely arise from any situation where we encounter a zero denominator, which isn't present, or if $ x $ equaled a specific value yielding inconsistencies.

Since $ x $ defined above does not provide an issue based on the above setup, the aforementioned responses do not depict derive conditions; however, if you meant to assert considerations based on conditions that produce unattainable situations outside nil interaction with $ x $, this would indicate recognizing infinite states meaning acknowledging $ x = 0 $ (in where not contributed) to restrict around that in lack of clear rationalized approaches yielded from foundational examples provided.

Thus based on traditional notional framework mechanics at best in equity to establish thorough clarity where you are focused primarily:

The appropriate response for an undefined condition assumed in response might be: $ x \neq 0 $.

This would highlight highlights expressions under control that signify lack of supply in working toward unresolved iterations by pointing signaling logically where potential miscommunication might exist to actualize otherwise interactively responsive loops.