To evaluate the expression \( 2.14x - 42.9 \) for \( x = 22.4 \), we will substitute \( 22.4 \) for \( x \) in the expression.
First, we calculate:
\[ 2.14 \times 22.4 \]
\[ 2.14 \times 22.4 = 47.936 \]
Next, we subtract \( 42.9 \) from \( 47.936 \):
\[ 47.936 - 42.9 = 5.036 \]
Therefore, the value of the expression \( 2.14x - 42.9 \) when \( x = 22.4 \) is:
\[ \boxed{5.036} \]