[Music] welcome to math with mr j [Music] in this video i'm going to cover how to solve one-step inequalities now one-step inequalities are just like one-step equations we need to isolate the variable which means get it by itself by using the inverse or opposite operation remember keep everything balanced so whatever you do to one side you have to do to the other the difference between inequalities and equations are the number of solutions so in our four examples these are going to have an infinite amount of solutions an equation is going to have exactly one solution so you'll see what i mean as we go through the four examples there on the screen now we do need to remember we flip the inequality symbol when we multiply or divide both sides by a negative number and we have one example of that in this video so let's jump into number one where we have y plus seven is less than eight so we need to isolate our variable of y we're adding seven to y so the opposite would be to subtract seven so let's subtract seven from that side and that's going to cancel those 7s out and isolate our y now whatever we do to one side we have to do to the other so if we subtracted 7 on the left we need to subtract 7 on the right and we end up with y is less than 8 minus 7 is 1. so here is our answer y is less than 1. so any number less than 1 would be a solution to that inequality and let's try and test one out here so zero is less than one let's see if that works let's plug in zero for y so we'll have zero plus seven is less than eight well zero plus seven is seven and seven is less than eight so zero was a solution along with anything else less than one an infinite amount of solutions on to number two where we have x divided by five is greater than or equal to three so we're dividing by five the opposite of dividing by five would be multiplying by five so let's multiply both sides by five the 5's on the left cancel out isolating the x and we have x is greater than or equal to 3 times 5 is 15. so x has to be greater than or equal to 15 in order to be a solution to that inequality so let's try something out that's greater than 15. let's try 20. 20 divided by 5 is greater than or equal to 3 so 20 divided by 5 is 4 4 is greater than or equal to 3 so that's true 20 would be a solution now 15 is included in the solutions for number 2 because it's an or equal to inequality on to number 3 where we have 14 is greater than or equal to n minus 11. so we need to isolate the n 11 is being subtracted from n so the opposite would be adding 11. so let's add 11 to both sides in order to isolate the n and keep everything balanced so n is isolated and 14 plus 11 is 25. so 25 is greater than or equal to n so n has to be less than 25 there or equal to 25 so let's test something out and see if it works let's do 20. 20 is less than 25 so we will plug 20 in for n so we have 14 is greater than or equal to 20 minus 11 is 9 and that is true so 20 would be a solution along with anything equal to or less than 25 so this is our final answer for number three and lastly number four we have negative six times r is less than 36 so we're multiplying r by a negative six the opposite of multiplying by negative six would be to divide by negative six so let's divide both sides by negative six that cancels the negative sixes out on the left isolating the r and we needed to do it to both sides to keep everything balanced so we're left with r and we need to flip the inequality sign when we multiply or divide both sides by a negative so we need to flip that sign and 36 divided by negative six is negative six so r is greater than negative six so anything greater than negative six is going to make that inequality true it's going to be a solution so let's try out negative 2. negative 2 is greater than negative 6 so let's plug that in negative 6 times negative 2 is less than 36 well negative 6 times negative 2 is a positive 12 which is less than 36 so negative 2 would be a solution along with anything else that is greater than negative six now the reason we flip that inequality sign is because flipping the sign will make the inequality true without flipping it we're actually going to get incorrect solutions the opposite of what we want and i go into further depth about why we flip that sign and more examples in some different videos i'll drop those links down in the description so there you have it there's how you solve one-step inequalities i hope that helped thanks so much for watching until next time peace