To solve the equation \( 10 + \sqrt{10x - 1} = 13 \), follow these steps:
- Subtract 10 from both sides of the equation:
\[ \sqrt{10x - 1} = 13 - 10 \] \[ \sqrt{10x - 1} = 3 \]
- Square both sides to eliminate the square root:
\[ (\sqrt{10x - 1})^2 = 3^2 \] \[ 10x - 1 = 9 \]
- Add 1 to both sides:
\[ 10x = 9 + 1 \] \[ 10x = 10 \]
- Divide by 10:
\[ x = \frac{10}{10} \] \[ x = 1 \]
Now, let's verify the solution:
Substituting \( x = 1 \) back into the original equation:
\[ 10 + \sqrt{10(1) - 1} = 10 + \sqrt{10 - 1} = 10 + \sqrt{9} = 10 + 3 = 13 \]
The equation holds true, so the solution is:
\[ \boxed{1} \]