Travis has decided to budget his spending money he can spend no more than $143.15 every month he also decided to spend 5.2 times as much money on video games as he spends on movies

This is an inequality equation because of the words "spend no more than"

Let:
x = amount he spends on movies
5.2x = amount he spends on video games

Amount spent on movies and video games should be less than or equal to $143.15

Equation would be:

x + 5.2x < 143.15
6.2x       < 143.15
÷6.2           ÷ 6.2  
     x       < 23.09

x should be less than $23.09. Let us assume that  x = 23.

x + 5.2x < 143.15

23 + 5.2(23) <  143.15
23 + 119.60 < 143.15
142.60         < 143.15   This makes the inequality true.

If x is more than 23.09, then Tom will exceed his budget.