Question

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

5/2x−8−1=9 and x≠−4

5/2x−8=9 and x≠−8

5/2x−8−1=9 and x≠4

5/2x−8−1=9 and x≠8

Answer 1

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

1. Simplifying the equation:
\[
\frac{5}{2}x - 9 = 9
\]

2. Adding 9 to both sides:
\[
\frac{5}{2}x = 18
\]

3. Multiplying both sides by \( \frac{2}{5} \):
\[
x = \frac{2}{5} \times 18 = \frac{36}{5} = 7.2
\]

Next, we want to express this as two equations. The original equation remains, and we can state that \( x \) is not equal to a value that would make any terms undefined.

Since this is a linear equation, there are no restrictions except for the values that would invalidate the original equation. In this case, there are no defined exclusions. For the options given, none directly relate to the equation's restrictions.

Considering the options:

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

The equation simplifies to \( \frac{5}{2}x - 9 = 9 \). Thus, we can write the final statement as:

\[
\frac{5}{2}x - 9 = 9 \text{ and } x = \frac{36}{5}
\]

Revisiting your answers, none of the choices correctly convey the conclusion we derived. The question may have intended to provide a value for \( x \) that was incorrect or misunderstanding of domain restrictions based on context.

Hence, the correct representation for what we can safely conclude in standard format would simply present the solution \( x = \frac{36}{5} \) and acknowledge that there aren't any excluded values unless specified.

Unfortunately, none of the provided options accurately represent the answer derived from the equation provided.