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

Answer 1

To rewrite the equation \( \frac{5}{2}x - 8 - 1 = 9 \) as two equations joined by "and," we need to isolate the variable \( x \).

Starting with the equation:

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

We simplify it:

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

Now, we add 9 to both sides:

\[
\frac{5}{2}x = 18
\]

Next, we'll multiply both sides by \( \frac{2}{5} \):

\[
x = \frac{2}{5} \cdot 18 = \frac{36}{5}
\]

Now, we can rewrite the equation as:

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

However, in looking at the responses provided, it seems those options do not include the correct isolated value along with a suitable condition. Therefore, the correct answer in this limited context of the options given can be:

\[
\frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq -4
\]

But **the specific values of \( x \)** derived from the equation should be confirmed or cross-checked in other contexts or options given.