To solve the inequality \( 5(-2 + x) < 3x + 2 \), first distribute the 5 on the left side:
\[ 5(-2) + 5x < 3x + 2 \] \[ -10 + 5x < 3x + 2 \]
Next, let's isolate the variable \( x \). Start by subtracting \( 3x \) from both sides:
\[ -10 + 5x - 3x < 2 \] \[ -10 + 2x < 2 \]
Now, add 10 to both sides:
\[ 2x < 2 + 10 \] \[ 2x < 12 \]
Finally, divide both sides by 2:
\[ x < 6 \]
Thus, the solution to the inequality is:
\[ \boxed{x < 6} \]