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# One-step inequalities: -5c ≤ 15

CCSS.Math:

## Video transcript

solve for C and graph the solution we have negative 5c is less than or equal to 15 so negative 5c is less than or equal to 15 I just rewrote it a little bit bigger so if you want to solve for C we just want to isolate this C right over here on maybe on the left hand side we have its right now being multiplied by negative 5 so the best way to just have a C on the left hand side is we can multiply both sides of this inequality by the inverse of negative 5 or by negative 1/5 and let me let me just so we want to multiply negative 1/5 times negative 5c and we also want to multiply 15 times negative 1/5 I'm just multiplying both sides of the inequality by the inverse of negative 5 because when this will cancel out with the negative 5 and leave me just with C now I didn't draw the inequality here because we have to remember if we multiply or divide both sides of an inequality by a negative number you have to flip the inequality and we are doing that we are multiplying both sides by negative 1/5 which is the equivalent of dividing both sides by negative 5 so we need to turn this from a less than or equal to a greater than or equal and now we can proceed solving for C so negative 1/5 5th times negative 5 is 1 so the left-hand side is just going to be C is greater than or equal to 15 times negative 1/5 that's the same thing as 15 divided by negative 5 and so that is negative 3 so our solution is C is greater than or equal to negative 3 and let's graph it so that is my number line let's say that is 0 negative 1 negative 2 negative 3 and then I could go above 1/2 and so C is greater than or equal to negative 3 so it can be equal to negative 3 so I'll fill that in right over there let me do it in a different color so I'll fill it in right over there and then it's greater than as well so it's all of these values I am I am filling in in green and you can verify that it works in the original inequality pick something that should work well 0 should work 0 is one of the numbers that we've filled in negative five times zero is zero which is less than or equal to 15 it's less than 15 now let's try a number that's outside of it and I haven't drawn it here I could continued with the number line in this direction you would have a negative 4 here negative 4 should not be included and let's verify that negative 4 doesn't work negative 4 times negative 5 is positive 20 and positive 20 is not less than 15 so it's good that we did not include negative 4 so this is our solution this is it this is that solution graphed now I wanted to do that in that other green color here you go that's what it looks like