Question

Rewrite the equation 5/2x−8 −1=9 as two equations joined by “and.”(1 point)
5/2x−8 −1=9 and x≠8
5/2x −8=9 and x≠−8
5/2x −8−1=9 and x≠−4
5/2x −8−1=9 and x≠4

Answer 1

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

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

2. Next, isolate the term with \( x \):
\[
\frac{5}{2}x = 9 + 9
\]
\[
\frac{5}{2}x = 18
\]

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

So we can express \( \frac{5}{2}x - 9 = 9 \) in two equations as:

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

However, the options you provided do not include \( x \neq 8 \), which reflects the original context rather than being derived from the equation.

Let's check the provided options:

1. \( \frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq 8 \)
2. \( \frac{5}{2}x - 8 = 9 \text{ and } x \neq -8 \)
3. \( \frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq -4 \)
4. \( \frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq 4 \)

The first equation simplifies to \( \frac{5}{2}x - 9 = 9 \), and it correctly states that \( x \) can take any value except 8. The option that stands out based on the context of the initial equation is:

\[
\frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq 4
\]

Therefore, the correct rewritten form of the equation is:

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

Please note that there seems to be some inconsistency with the options provided and the restrictions derived. Thus, I recommend verifying the context of constraints on \( x \).