Question

Variable Expressions in Denominators Quick Check
1 of 51 of 5 Items
Question
Rewrite the equation 52x−8−1=9
as two equations joined by “and.”(1 point)
Responses

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−8−1=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≠−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

Answer 1

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

1. Start with the equation:
\[
\frac{5}{2}x - 8 - 1 = 9
\]
Simplify it:
\[
\frac{5}{2}x - 9 = 9
\]
Add \( 9 \) to both sides:
\[
\frac{5}{2}x = 18
\]
To solve for \( x \), multiply both sides by \( \frac{2}{5} \):
\[
x = \frac{2}{5} \times 18 = \frac{36}{5} = 7.2
\]

2. Since we have a fractional expression, we should clarify the restrictions. Because of the term \( \frac{5}{2}x - 8 \), we need to ensure that the denominator is not equal to zero. However, in this case \( \frac{5}{2} \) is never zero for any valid \( x \).

Thus, the final rewritten form of the equation with restrictions would be:
\[
\frac{5}{2}x - 9 = 9 \quad \text{and} \quad x \text{ can be any real number.}
\]

Among the provided options, none of them correctly represent the transformation and restrictions; therefore, it appears that none of the responses are appropriate to this problem.

The most appropriate correct response would be:
\[
\frac{5}{2}x - 9 = 9 \quad \text{and} \quad \text{no restrictions on } x.
\]