To rewrite the equation \( \frac{5}{2}x - 8 - 1 = 9 \) as two equations joined by "and," we can first isolate the fractional part and then express the equation correctly.
Starting with the given equation:
\[ \frac{5}{2}x - 8 - 1 = 9 \]
This simplifies to:
\[ \frac{5}{2}x - 9 = 9 \]
Next, we solve for \( x \):
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Add 9 to both sides: \[ \frac{5}{2}x = 18 \]
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Multiply both sides by \( \frac{2}{5} \): \[ x = \frac{2 \cdot 18}{5} = \frac{36}{5} = 7.2 \]
So, the correct way to express this problem in the desired format is:
\[ \frac{5}{2}x - 8 - 1 = 9 \text{ and } x = \frac{36}{5} \]
Since the question did not provide any restrictions on \( x \) apart from that it simplifies, the "and" condition would simply state that \( x \) must equal \( \frac{36}{5} \).
However, among provided options, let's analyze the closest possible valid condition which ensures no undefined behavior:
- \( x \neq -4 \) would not necessarily relate to the function derived here and could lead to confusion.
- Other options could be a misinterpretation based on the initial arrangement of the equation.
For clarity: If no other conditions or variations must be simply matched from your options:
\(\frac{5}{2}x - 9 = 9\) and \(x\) solves to \(\frac{36}{5}\) as an answer.
So, the closest and most apparent form for a simple synthesized answer without conflicts would be:
Without additional context or restrictions, please clarify if any other restrictions on \(x\) would have to meet specific exclusions in mathematical terms.
1 answer