Question

Rewrite the equation 52x−8−1=9
5
2
𝑥
−
8
−
1
=
9
as two equations joined by “and.”(1 point)
Responses

52x−8=9
5
2
𝑥
−
8
=
9
and x≠−8
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
5
2
𝑥
−
8
−
1
=
9
and x≠−4
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
5
2
𝑥
−
8
−
1
=
9
and x≠8
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
5
2
𝑥
−
8
−
1
=
9
and x≠4

Answer 1

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

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

2. Combine like terms:
\[
\frac{5}{2} x - 9 = 9
\]

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

4. Multiply both sides by \( \frac{2}{5} \) to solve for \( x \):
\[
x = \frac{2}{5} \cdot 18 = \frac{36}{5}
\]

Now, we can represent this as two equations. The equation simplifies to \( \frac{5}{2} x - 9 = 0 \) and we have identified that \( x = \frac{36}{5} \).

Thus, we can write:
\[
\frac{5}{2} x - 9 = 0 \quad \text{and} \quad x = \frac{36}{5}
\]

However, looking at the option that matches the original form, it can be expressed in a similar format as:

\[
\frac{5}{2} x - 8 - 1 = 9 \quad \text{and} \quad x \neq 8
\]

Thus, the correct choice aligns with the first simplification step before final adjustments, ensuring to match the correct response format. Therefore, the rewriting can be:

\[
\frac{5}{2} x - 8 = 9 \quad \text{and} \quad x \neq -4
\]

However, it's important to highlight that the equation's exact interpretation may vary based on options available as provided in your question. The key point is to express it as two separate valid equations logically connected by "and."