To rewrite the given equation \( \frac{5}{2}x - 8 - 1 = 9 \) as two equations joined by "and," we first simplify the equation.
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Combine like terms on the left side: \[ \frac{5}{2}x - 9 = 9 \]
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Next, isolate the term with \( x \): \[ \frac{5}{2}x = 9 + 9 \] \[ \frac{5}{2}x = 18 \]
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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:
- \( \frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq 8 \)
- \( \frac{5}{2}x - 8 = 9 \text{ and } x \neq -8 \)
- \( \frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq -4 \)
- \( \frac{5}{2}x - 8 - 1 = 9 \text{ and } x \neq 4 \)
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 \( x \).
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