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

Question

Responses

52x−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

52x−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

52x−8=9 and x≠−8
Start Fraction 5 over 2 x minus 8 End Fraction equals 9 and x does not equal negative 8

52x−8−1=9 and x≠4

Answer 1

To rewrite the equation \(\frac{5}{2x-8} - 1 = 9\) as two equations joined by "and," we first isolate the rational expression and then handle the condition for the variable.

1. Start with the original equation:
   \(\frac{5}{2x-8} - 1 = 9\)

2. Rearranging gives us:
   \(\frac{5}{2x-8} = 10\)

3. Now we express it as two equations:
   \(\frac{5}{2x-8} = 10\) and \(2x - 8 \neq 0\) (to avoid division by zero)

From \(2x - 8 \neq 0\), we find \(x \neq 4\).

Thus, the correct response is:
\(\frac{5}{2x-8} = 10\) and \(x \neq 4\) (not present in the options you provided).

Therefore, based on the provided options, the correct transformation would be:
\(\frac{5}{2x-8} - 1 = 9\) and \(x \neq 4\).