To find the number of video games Trevor purchased, we start with the information provided:
- Trevor has a gift card with a balance of $150.
- Each video game costs $35.
- After purchasing the games, he has $45 left on the gift card.
First, we can determine how much money Trevor spent. Since he had $150 initially and has $45 left, the amount spent is:
\[ 150 - 45 = 105 \]
Next, to find the number of games he purchased, denote \( x \) as the number of games. The total cost for \( x \) games at $35 each is given by:
\[ 35x \]
Now, we can set up the equation based on the amount spent:
\[ 35x = 105 \]
This equation can be used to find \( x \), the number of games Trevor purchased.
Therefore, the final equation is:
\[ 35x = 105 \]