Question
Rewrite the equation 5/2x-8 – 1 = 9 as two equations joined by “and”
A. 5/2x-8 – 1 = 9 and x ≠ 8
B. 5/2x-8 – 1 = 9 and x ≠ -4
C. 5/2x-8 – 1 = 9 and x ≠ 4
A. 5/2x-8 – 1 = 9 and x ≠ 8
B. 5/2x-8 – 1 = 9 and x ≠ -4
C. 5/2x-8 – 1 = 9 and x ≠ 4
Answers
Answered by
GPT-4o mini
To rewrite the equation \( \frac{5}{2}x - 8 - 1 = 9 \) as two equations joined by "and," we first need to simplify and solve the primary equation.
1. Simplify the equation:
\[
\frac{5}{2}x - 9 = 9
\]
2. Add 9 to both sides:
\[
\frac{5}{2}x = 18
\]
3. Multiply both sides by \( \frac{2}{5} \) to solve for \( x \):
\[
x = \frac{2 \times 18}{5} = \frac{36}{5}
\]
Now, since the equation is \( \frac{5}{2}x - 9 = 9 \), we can specify that this solution holds as long as \( x \) is not equal to a particular constraint.
None of the options directly reflect our solution since we didn't derive any restrictions or exclusions from the original equation. However, common algebraic mistakes might yield extraneous roots, so verify for any standard exclusions.
Among the provided options:
- A: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 8 \)
- B: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq -4 \)
- C: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 4 \)
None of these restrictions seem relevant, but the actual formulation can be clearly stated as:
\[
\frac{5}{2}x - 9 = 9 \text{ and } x = \frac{36}{5}
\]
Thus, if we have to choose from the options given above, there seems to be a misunderstanding of what exclusions need to be emphasized. Assuming typical simplifications, the answer cannot be one of the existing choices.
We can represent the main equation together with a validation requirement instead; thus, despite incorrect exclusions, the solved equation stands as:
\[
\frac{5}{2}x - 9 = 9 \text{ and } x = \frac{36}{5}
\]
Should you reframe this perspective, kindly double-check the assumptions noted in the initial equations, as provided "and" options might limit context exhibited from true solution.
1. Simplify the equation:
\[
\frac{5}{2}x - 9 = 9
\]
2. Add 9 to both sides:
\[
\frac{5}{2}x = 18
\]
3. Multiply both sides by \( \frac{2}{5} \) to solve for \( x \):
\[
x = \frac{2 \times 18}{5} = \frac{36}{5}
\]
Now, since the equation is \( \frac{5}{2}x - 9 = 9 \), we can specify that this solution holds as long as \( x \) is not equal to a particular constraint.
None of the options directly reflect our solution since we didn't derive any restrictions or exclusions from the original equation. However, common algebraic mistakes might yield extraneous roots, so verify for any standard exclusions.
Among the provided options:
- A: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 8 \)
- B: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq -4 \)
- C: \( \frac{5}{2}x - 8 - 1 = 9 \) and \( x \neq 4 \)
None of these restrictions seem relevant, but the actual formulation can be clearly stated as:
\[
\frac{5}{2}x - 9 = 9 \text{ and } x = \frac{36}{5}
\]
Thus, if we have to choose from the options given above, there seems to be a misunderstanding of what exclusions need to be emphasized. Assuming typical simplifications, the answer cannot be one of the existing choices.
We can represent the main equation together with a validation requirement instead; thus, despite incorrect exclusions, the solved equation stands as:
\[
\frac{5}{2}x - 9 = 9 \text{ and } x = \frac{36}{5}
\]
Should you reframe this perspective, kindly double-check the assumptions noted in the initial equations, as provided "and" options might limit context exhibited from true solution.