To solve the equation \( 2^1 + 2x = 0.04 \times 10^1 + 2x \), we can start by simplifying each side.
Calculate \( 2^1 \): \[ 2^1 = 2 \]
Calculate \( 0.04 \times 10^1 \): \[ 0.04 \times 10^1 = 0.04 \times 10 = 0.4 \]
Now, substitute these values back into the equation:
\[ 2 + 2x = 0.4 + 2x \]
Next, we can subtract \( 2x \) from both sides:
\[ 2 = 0.4 \]
This statement is not true. Therefore, we conclude that there are no values of \( x \) that would satisfy the original equation.
Thus, the equation has no solution.