Solving a Two-Step Inequality (Example Involves Flipping the Inequality Symbol) | Math with Mr. J

[Music] welcome to math with Mr J in this video I'm going to cover how to solve a twostep inequality now when we solve twostep inequalities we want to isolate the variable get it by itself on one side of the inequality we do that by using inverse operations so this is very similar to solving twostep equations if you can solve an equation you can solve an inequality one thing that we need to be aware of though when it comes to inequalities remember we flip the inequality symbol when multiplying or dividing both sides by a negative let's jump into our example where we have y / -2 + 5 is greater than or equal to 9 now here just like we would do if this was a two-step equation we want to undo the the addition first we go in the reverse order of operations to undo the operations and isolate the variable so we need to undo the addition first and then the division here the inverse operation of addition is subtraction so let's subtract five from the left side of the inequality whatever we do to one side of an inequality we must do to the other in order to to keep it balanced so subtract five from the right side as well now on the left side these fives cancel each other out so we have y / -2 is greater than or equal to and then on the right 9 - 5 gives us 4 so now we have y / -2 is greater than or equal to 4 now since Y is being divided by -2 we need to undo that division using the inverse operation that's multiplication so let's multiply the left side by -2 whatever we do to one side we must do to the other so multiply the right side by -2 as well now remember when we multiply or divide both sides of an inequality by a negative the inequality symbol flips it changes Direction so on the left these - tws cancel each other out Y is now isolated the inequality symbol flips and then on the right 4 * -2 gives us8 so Y is less than or equal to -8 so y can be any value less than or equal to 8 now as far as that inequality symbol Sy flipping basically as soon as we multiplied both sides by a negative -2 for this example that inequality symbol flips in order to keep the inequality true lastly let's check this by plugging in a value that is less than or equal to -8 for y and seeing if it works so we can see if we are correct here let's use -10 that's less than 8 and since we are dividing by -2 that will work nicely there then we have + 5 is greater than or equal to 9 -10 / -2 gives us 5 and then 5 + 5 gives us 10 10 is greater than or equal to 9 so that does work we are correct here Y is less than or equal to 8 and then since y can be equal to8 let's try that as well and we will do this mentally so we have8 / -2 + 5 -8 / -2 gives us 4 4 + 5 gives us 9 and 9 is greater than or equal to 9 so that works as well so there you have it there's how to solve a two-step inequality now now that was just one example I have a link to another example down in the description or if you want a few more examples I have a longer video in the description as well so use whatever works best for you I hope that helped thanks so much for watching until next time peace