Analyzing structure with linear inequalities: balls

a bag has more green balls and blue balls and there is at least one blue ball let B represent the number of blue balls and let G represent the number of green balls let's compare the expressions to b + b + g which statement is correct so they make a bunch of comparisons between two b + b + g is it's greater than less than equal or not enough information to tell and so like always pause this video and see if you can figure it out on your own before we work through it together alright let's work through it together and let's see what information they are giving us so this first sentence they say a bag has more green balls and blue balls so we can translate that in math language as the number of green balls is greater than the number of blue balls it also says there is at least one blue ball so just translating that mathematically we know that B is going to be greater than or equal to 1 there's at least one but maybe more so B is greater than or equal to one so now let's see if we can somehow manipulate these so we can get to some reasonable sense of how B plus G compares 2 to B well there's a bunch of different ways that you could approach it you might find a way to approach it that is different than my way but the one that jumps out at me is well I know that G is greater than B and if I add a B to both sides on the left hand side I'm going to have a B + G and on the right hand side I'm going to have a B plus B and this right over here is 2 B so just like that I know I can keep the inequality if I'm doing the same thing to both sides if I'm adding or subtracting the same thing to both sides and so just from G is greater than B if you add B to both sides of that we can deduce that B + G is going to be greater than B plus B or it's just going to be greater than 2 B and that's all we need to do and let's see which of these choices match up to that so let's see all of these have to be on the left hand side so we could rewrite this as 2 B is less than B + G and that is that choice right over there