Question
Rewrite the equation 5/(2x - 8) - 1 = 9 as two equations joined by "and" (1 point) 5/(2x - 8) - 1 = 9 and x ne-4; 5/(2x - 8) - 1 = 9 and x ne4; 5/(2x - 8) - 1 = 9 and x ne8; 5/(2x - 8) = 9 and x ne-8
Answers
Answered by
GPT-4o mini
To rewrite the equation \( \frac{5}{2x - 8} - 1 = 9 \) as two equations joined by "and," we need to isolate the fraction on one side and also mention the restrictions on \( x \) that arise from the denominator.
1. Start with the original equation:
\[
\frac{5}{2x - 8} - 1 = 9
\]
2. Isolate the fraction by adding 1 to both sides:
\[
\frac{5}{2x - 8} = 10
\]
3. Now, the equation can be rewritten as:
\[
\frac{5}{2x - 8} = 10 \quad \text{and} \quad 2x - 8 \neq 0
\]
The second part means that \( 2x - 8 \) cannot be zero, which simplifies to:
\[
x \neq 4
\]
So, the final rewritten statement is:
\[
\frac{5}{2x - 8} = 10 \quad \text{and} \quad x \neq 4
\]
From the options you provided, the correct answer is:
\[
5/(2x - 8) = 9 \quad \text{and} \quad x \neq 4
\] (but with \( 10 \) instead of \( 9 \)).
1. Start with the original equation:
\[
\frac{5}{2x - 8} - 1 = 9
\]
2. Isolate the fraction by adding 1 to both sides:
\[
\frac{5}{2x - 8} = 10
\]
3. Now, the equation can be rewritten as:
\[
\frac{5}{2x - 8} = 10 \quad \text{and} \quad 2x - 8 \neq 0
\]
The second part means that \( 2x - 8 \) cannot be zero, which simplifies to:
\[
x \neq 4
\]
So, the final rewritten statement is:
\[
\frac{5}{2x - 8} = 10 \quad \text{and} \quad x \neq 4
\]
From the options you provided, the correct answer is:
\[
5/(2x - 8) = 9 \quad \text{and} \quad x \neq 4
\] (but with \( 10 \) instead of \( 9 \)).