Let the original number Uche thinks of be \( x \).
According to the problem, Uche adds 7 to the number and then doubles the result:
\[ 2(x + 7) = 34 \]
Now, we can solve for \( x \).
- Divide both sides by 2:
\[ x + 7 = 17 \]
- Subtract 7 from both sides:
\[ x = 17 - 7 \]
\[ x = 10 \]
So, the original number Uche thinks of is \( 10 \).