 In this video, we provide the solution to question number five from practice exam number two from math 1050 In which case we have to solve the absolute value in the quality the absolute value of 5 minus 2x is greater than equal to 1 Some things to remember with absolute values absolute value is never negative It's always positive or zero Therefore if you have an absolute value that's greater than equal to a negative Then you'd get all real numbers that also be true if you had zero because again absolute value can't be smaller than zero So we could have all real numbers That's not happening in this situation. You should also be cautious that absolute value can never be less than or equal to a negative You'd get no solution Similar things happen there now. That's not the case on this exact exercise here We just want to be greater than or equal to one so what we can do is we can consider the two cases There's the positive case where five minus two x is greater than equal to one or There's the negative case where you have five minus two x is less than or equal to negative one We do have to flip the sign in the negative case like so and then we proceed to solve these these two inequalities They don't exactly overlap But nonetheless the process of solving it's gonna be the same and by the in either of the two cases You're gonna subtract five from both sides On the original positive case then you end up with negative 2x is greater than equal to negative 4 and then in the Original negative case you're then gonna get negative 2x is less than in this case negative 6 Now we're gonna divide both sides. We'll both inequalities on both sides by negative 2 What's good for the goose is good for the gander and which case in the end? We end up with x is because we divided by negative 2 the sign will switch around so we get x is less than in This case a positive 2 or in the other case We're gonna get x again. We divided by negative 2 so it flips the inequality round x is greater than 3 Negative 6 divided by negative 2 is a positive 3 So we want x is less than 2 or x is greater than 3 the first inequality here Does become an interval negative infinity to 2 inclusive because we do have We're allowed equal to 2 less than 2 or equal to equal to 2 the or symbol or I should say the or here means We're taking a union and then we want also x is greater than or equal to 3 so bracket 3 towards infinity That would be our solution in that situation For which then we can quickly see that the correct answer would that be choice a