Rewrite the equation 5/2x−8−1=9 as two equations joined by “and.”(1 point)

Question

Responses

5/2x−8−1=9 and x≠4
Start Fraction 5 over 2 x minus 8 End Fraction minus 1 equals 9 and x does not equal 4

5/2x−8−1=9 and x≠8
Start Fraction 5 over 2 x minus 8 End Fraction minus 1 equals 9 and x does not equal 8

5/2x−8=9 and x≠−8
Start Fraction 5 over 2 x minus 8 End Fraction equals 9 and x does not equal negative 8

5/2x−8−1=9 and x≠−4

Answer 1

To rewrite the equation \( \frac{5}{2}x - 8 - 1 = 9 \) as two equations joined by "and," we first simplify the original equation:

1. Combine like terms: \[ \frac{5}{2}x - 9 = 9 \]

2. Add 9 to both sides to isolate the term with \( x \): \[ \frac{5}{2}x = 18 \]

3. Solve for \( x \) by multiplying both sides by \( \frac{2}{5} \): \[ x = \frac{2}{5} \times 18 = \frac{36}{5} \]

Thus, we can rewrite the equation as follows: \[ \frac{5}{2}x - 8 - 1 = 9 \text{ and } x = \frac{36}{5} \]

However, we don't have conditions for \( x \) in the initial equation, so we could focus on stating the equation and confirming the derived solution.

The appropriate response from the options provided seems to involve indicating a value for \( x \) being equal to or not equal to something. None of the options directly includes the simplified equation as its second equation.

Thus, the best of the provided options aligns with the process that leads us to the derived solution, yet does not present it correctly. Nevertheless, here’s how it should have ideally read:

\[ \frac{5}{2}x - 8 - 1 = 9 , and , x = \frac{36}{5} \]

Since none exactly fit that format and given the nature of equations equating or being defined, select the option that best fits a reasonable response considering the options provided, with respect to conditions:

Note: None match correctly with the currently established solution for \( x \).

Answer 2

a,b,c or d

Answer 3

Given the original equation \( \frac{5}{2}x - 8 - 1 = 9 \) simplifies to \( \frac{5}{2}x - 9 = 9 \) and then solves to \( x = \frac{36}{5} \), let's evaluate the options based on that process. The key is whether they include valid conditions for \( x \) based on the structure provided:

Here are the choices:

A) \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 4 \)

B) \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 8 \)

C) \( \frac{5}{2}x - 8 = 9 \) and \( x \neq -8 \)

D) \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq -4 \)

Evaluating the options:

The equation \( \frac{5}{2}x - 8 - 1 = 9 \) is correct and indicates all cases lead back not to having incapable values omitted erroneously. Hence, none adhere strictly to the variable condition.

However, with respect to logical relevance of equations:

• Choices that exclude values as potential irrelevancies, as informed through the solutions based on proper derivation:

None might explicitly reaffirm the computed \( x = \frac{36}{5} \).

But based on your request without deep error,

The closest logical choice is A because it carries the original form of the equation with an arbitrary exclusion.

Thus, the answer is: A) \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 4 \).

If more clarification or reasoning based on wrong placements is sought, explore any deeper conflation or disambiguation in the structured equation interpretations!

Answer 4

What happens when a value causes a denominator in a fraction to be equal to zero?(1 point)
Responses

There are infinite solutions.
There are infinite solutions.

The value of the equation becomes zero.
The value of the equation becomes zero.

This value is a solution to the equation.
This value is a solution to the equation.

This fraction is undefined.
This fraction is undefined.