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Conţinutul principal
Ora curentă:0:00Durata totală:4:32

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we have the inequality 2/3 is greater than negative 4y minus 8 and 1/3 now the first thing I want to do here just because mixed numbers bother me they're actually hard to deal with mathematically they're easy to think about oh it's a little bit more than 8 let's convert this to a improper fraction so eight and 1/3 is equal to the denominator is going to be 3 3 times 8 is 24 plus 1 is 25 so this thing over here is the same thing as 25 over 3 let me just rewrite the whole thing so it's 2/3 is greater than negative 4y minus minus 25 minus 25 over 3 now the next thing I want to do just because dealing with fractions are a bit of a pain is multiply both sides of this inequality by some quantity that'll eliminate the fractions and the easiest one I could think of is multiply both sides by 3 that will get rid of the 3s in the denominator so let's multiply both sides of the equation by 3 that's the left-hand side and then I'm going to multiply the right-hand side 3 I put in parentheses like that and well one point that I want to point out is that I did not have to swap the inequality sign because I multiplied both sides by a positive number if the 3 was a negative number if I multiplied both sides by negative 3 or negative 1 or negative whatever I would have had to swap the inequality sign anyway let's simplify this so the left-hand side we have 3 times 2/3 which is just 2 2 is greater than and then we can distribute this 3 3 times negative 4y is negative 12y and then 3 times negative 25 over 3 is just negative 25 now we want to get all of our constant terms on one side of the inequality and all of our variable terms the only variable here is Y on the other side the Y is already sitting here so let's guess this 25 on the other side of the inequality and we can do that by adding 25 to both sides of this equation so let's add 25 to both sides of this equation adding 25 and the left-hand side 2 plus 25 is 27 we need 27 is greater than the right hand side of the inequality is negative 12y negative 12y and the negative 25 plus 25 those cancel out that was the whole point so we're left with 27 is greater than negative 12y now to isolate the Y we can multiply or think you can either multiply both sides by negative 1/12 or you could say let's just divide both sides by negative 12 now because I'm multiplying or dividing by a negative number here I'm going to need to swap the inequality so let me write this if I divide both sides of this equation by negative 12 then it becomes 27 over negative 12 is less than I'm swapping the inequality let me do this in a different color is less than is less than negative 12 y over negative 12 notice when I divide both sides of the inequality by a negative number I swap the inequality I swap the greater than becomes a less than when it was positive I could I didn't have to swap it so 27 divided by negative 12 well they're both divisible by 3 so we're going to get if we do the numerator the denominator by 3 we get negative 9 negative 9 over 4 is less than these cancel out Y so Y is greater than negative 9/4 or negative 9/4 is less than Y and if you wanted to write that let me write this so our answer is y is greater than negative 9/4 I just swapped the order or you could say negative 9/4 is less than Y or if you want to visualize that a little bit better 9/4 is 2 and 1/4 so we could also say Y is greater than negative 2 and 1/4 if we want to put it as a mixed number and if we wanted to graph it on the number line let me draw a number line right here real simple 1 maybe this is 0 negative 2 is right over let's say negative 1 negative 2 then say negative 3 is right there negative 2 and 1/4 is going to be right here and it's greater than so we're not going to include that in the solution set it's going to make an open circle right there and everything larger than that is a valid y is a that will satisfy the inequality