Can You Solve This Easy Peasy Inequality Problem #math

Added: 2026-05-27

[00:00:00]Okay, so the goal of this problem is to prove that this inequality is equivalent to the following inequality. So, how can we do that? The first method is that x squared is essentially the absolute value squared and y squared is the absolute value of y squared cuz we lay down our absolute value squared y absolute value squared. It would be the same thing, which is the absolute value minus absolute value value of y and then absolute value of x plus absolute value of y. This part is always positive. This part should be negative. Our difference of our absolute values here has less than or equal to zero. We can represent x squared minus y squared less than or equal to zero, which is x minus y x plus y less than or equal to zero, which is the same as x less than or equal to y and x is greater than or equal to negative y or is less than or equal to negative y and x is greater than or equal to y. This part is equivalent to saying that x is less than y or greater than negative y and x is less than or equal to negative y and greater than or equal to y. If y is greater than or equal to zero, this first inequality becomes x is less than or equal to y absolute value and less than negative absolute value. If however y is less than or equal to zero, the second inequality becomes x then less than or equal to y and greater than or equal to negative absolute value y, which is equivalent to the route to x absolute value is less than or equal to absolute value of y.