Alright, let's solve the equation [tex]\(\frac{5}{8} = \frac{x-1}{9}\)[/tex] for the variable [tex]\(x\)[/tex] step-by-step.
### Step-by-Step Solution:
1. Set up the initial equation:
[tex]\[
\frac{5}{8} = \frac{x-1}{9}
\][/tex]
2. Eliminate the fractions by cross-multiplying:
To clear the fractions, we multiply both sides of the equation by the denominators of each fraction. This is known as cross-multiplying.
[tex]\[
5 \cdot 9 = 8 \cdot (x - 1)
\][/tex]
3. Perform the multiplications:
[tex]\[
45 = 8(x - 1)
\][/tex]
4. Distribute and simplify:
Distribute the 8 on the right side of the equation.
[tex]\[
45 = 8x - 8
\][/tex]
5. Isolate the variable [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], we first need to get rid of the [tex]\(-8\)[/tex] on the right side by adding 8 to both sides of the equation.
[tex]\[
45 + 8 = 8x - 8 + 8
\][/tex]
Simplify both sides:
[tex]\[
53 = 8x
\][/tex]
6. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by 8 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{53}{8}
\][/tex]
So, the solution for [tex]\(x\)[/tex] is:
[tex]\[
x = \frac{53}{8}
\][/tex]
### Final Answer:
[tex]\[
\frac{53}{8}
\][/tex]
This matches one of the answer choices provided, confirming our solution.
