Question

rewrite the equation 5/(2x-8)-1=9

Answer 1

To rewrite the equation \( \frac{5}{2x-8} - 1 = 9 \), we can start by isolating the fraction. Here's how to do it step by step:

1. Add 1 to both sides:
\[
\frac{5}{2x-8} = 9 + 1
\]
\[
\frac{5}{2x-8} = 10
\]

2. Next, we can eliminate the fraction by multiplying both sides by \( 2x - 8 \) (assuming \( 2x - 8 \neq 0 \)):
\[
5 = 10(2x - 8)
\]

3. Now, distribute the 10 on the right side:
\[
5 = 20x - 80
\]

4. To isolate \( x \), add 80 to both sides:
\[
5 + 80 = 20x
\]
\[
85 = 20x
\]

5. Finally, divide both sides by 20:
\[
x = \frac{85}{20}
\]
Simplifying further gives:
\[
x = \frac{17}{4}
\]

So, the rewritten equation shows that \( x = \frac{17}{4} \). If you want the equation in terms of \( x \) only, we can also express it as follows:

\[
\frac{5}{2x-8} = 10
\]
This is an alternative representation of the original equation after rearranging.