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

A. 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 4

B. 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

C. 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

D. 52x−8−1=9 and x≠8

1 answer

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

Let's simplify the original equation:

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

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

Now we can express this using "and." The equation already simplifies directly to: \[ \frac{5}{2}x - 9 = 9 \text{ and } x \neq 4 \]

We now analyze the options provided to see which reflects this:

  • A: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 4 \) (matches but incorrect equation)
  • B: \( \frac{5}{2}x - 8 = 9 \) and \( x \neq -8 \) (does not match)
  • C: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq -4 \) (matches but incorrect)
  • D: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 8 \) (not correct)

The proper answer, assuming simplification gives us an equivalent representation without losing meaning should echo the isolation done earlier.

The correct response effectively reconstructs the full expression intended — meaning that the correct choice considering valid expansion combined with restrictions within choices is C, only if an indicative adjustment of constants appears.