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 start by isolating the fraction:

1. Add 1 to both sides:
   \(\frac{5}{2x - 8} = 10\)

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

3. Identifying restrictions on \(x\): The denominator cannot be zero, so set \(2x - 8 \neq 0\):
   \(2x \neq 8\) or \(x \neq 4\)

Putting these together, the rewritten format is:

\(\frac{5}{2x - 8} = 10 \text{ and } x \neq 4\)

So the correct response would be:

\(\frac{5}{2x - 8} = 10 \text{ and } x \neq 4\)