To ensure the equation has infinite solutions, we need to create a right side of the equation that is equivalent to the left side when simplified.
Starting with the left side:
\[ -5x + 3x - 2 = -2x - 2 \]
Now, to express the right side so that both sides are equal, we can create an expression that simplifies to the left side. A simple way to do this is to use the same expression we have on the left side.
So, we could write:
\[ -5x + 3x - 2 = -2x - 2 \]
We can set the right-hand side as:
\[ -2x - 2 \]
Thus, the complete equation would be:
\[ -5x + 3x - 2 = -2x - 2 \]
This equation has infinite solutions, because any value of \(x\) will satisfy both sides of the equation.