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Current time:0:00Total duration:3:47

Inequalities with variables on both sides (with parentheses)

Video transcript

solve for X and we have 5x plus 7 is greater than 3 times X plus 1 so let's just try to isolate X on one side of this inequality but before we do that let's just simplify this right-hand side so we get 5x plus 7 is greater than let's distribute this 3 so 3 times X plus 1 is the same thing as 3 times X plus 3 times 1 so it's going to be 3x plus 3 times 1 is 3 now if we want to put our X's on the left hand side we can subtract 3x from both sides that'll get rid of this 3x on the right hand side so let's do that let's subtract 3x from both sides and we get on the left-hand side 5x minus 3x is 2x plus 7 is greater than 3x minus 3x those cancel out that was the whole point behind subtracting 3x from both sides is greater than 3 is greater than 3 now we can subtract 7 from both sides to get rid of this positive 7 right over here so let's subtract let's subtract 7 from both sides and we get on the left-hand side 2x plus 7 minus 7 is just 2x is greater than 3 minus 7 which is negative 4 and then let's see we have 2x is greater than negative 4 if we just want an X over here we can divide both sides by 2 since 2 is a positive number we don't have to swap the inequality so let's just divide both sides by 2 and we get X is greater than negative 4 divided by 2 is negative 2 so the solution will look like this draw the number line I can draw a straighter number line than that there we go still not that great but it'll serve our purposes so let's say that's negative 3 negative 2 negative 1 0 1 2 3 X is greater than negative 2 it does not include negative 2 it is not greater than or equal to negative 2 so we have to exclude negative 2 and we exclude negative two by drawing an open circle at negative two but then all of the values greater than that are valid X's that would solve that would satisfy this inequality so anything above it anything above it will work and let's just try let's try this just try something that should work and then let's try something else that will shouldn't work so zero should work it is greater than negative two it's right over here so let's verify that five times zero plus seven should be greater than three times zero plus one so this is seven because this is just a zero seven should be greater than 3 right 3 times 1 so 7 should be greater than 3 and it definitely is now let's try something that should not work let's try negative 3 so 5 times negative 3 5 times negative 3 plus 7 let's see if it's greater than 3 times negative 3 plus 1 so this is negative 15 plus 7 is negative 8 that is negative 8 let's see if that is greater than negative 3 plus 1 is negative 2 times 3 is negative 6 negative 8 is not is not greater than negative 6 negative 8 is more negative than negative 6 it's less than so it's good that negative 3 didn't work because we didn't include that in our solution set so we tried something that is in our solution set and it did work and something that's not and it didn't work so we're feeling pretty good