Question

Rewrite the equation 52x−8−1=9 as two equations joined by “and.”(1 point) 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=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 Start Fraction 5 over 2 x minus 8 End Fraction minus 1 equals 9 and x does not equal 4 52x−8−1=9 and x≠8

Answer 1

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

1. The equation can be simplified to:
\[
\frac{5}{2}x - 9 = 9
\]

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

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

Next, we should also find any restrictions on \( x \). In the context of the original equation, \( \frac{5}{2}x - 8 - 1 = 9 \), we notice that \( x \) must not equal the values that make the denominator zero if we had a fraction. However, since there are no such restrictions in this case, we don't need a restriction on \( x \).

The cleaned equation is then:
\[
\frac{5}{2}x - 9 = 9 \quad \text{and} \quad x \text{ has no restrictions}
\]

Since the provided original equation implies no restrictions on \( x \), the conclusion is:

Final response:
\[
\frac{5}{2}x - 9 = 9 \quad \text{and} \quad x \text{ has no restrictions}
\]

Among the given options, none match the formatting requested. The correct interpretation would be represented simply as the equation derived and the absence of restrictions unless specified otherwise.