VIDEO5: x-5y>20 FLIP INEQUALITY sign
Math
FLIP INEQUALITY sign problem-solving example
Our next example, X -5 Y, greater than or equal to 20. So remember in order to solve this inequality, the first step is to circle the sign, the number and the Y then we're going to put a box around the side that has the Y value. Our goal. Is to get rid. Of everything. Inside the box. Except Y, except our letter Y so we are going to leave this for last. So first we have to start out getting rid of the X in front of this X, there's an imaginary. If you see nothing, it means that there is an imaginary plus sign. We're going to do the opposite. If you see a plus sign, then you're going to put a minus sign. So minus X goes here. M minus X goes also over here on the other side of the wall. We're going to bring down everything that we circled.
A positive X means that there's a positive one in front of the X, a negative X means that there's a negative one in front of the X, a positive one X means that I have $1 in my pocket, a negative one X means that I have to give you a dollar. If I have a dollar in my pocket, I have to give you a dollar. That means I have nothing. So we put nothing here, the positive one, and the negative one cancel each other out. I'm going to bring down everything I've seen inside the circle, the negative the 5 and the Y might the equality symbol. And these two are not like terms. So all you do is write them side by side. Normally I would put the 21st, but you know that the X value has to go first. So I'm going to put my negative and my X first. And this is a positive 20. So I'm going to put a positive 20. We still have to get rid of everything except the Y next to the Y is a negative 5.
In between the Y negative 5, there's an imaginary multiplication symbol. The opposite of multiply is to divide. So I'm going to divide everything that I see. By negative 5. Now here's the tricky part. With an inequality. Whenever. I divide. Or. Multiply. By a negative. Number. Then. I have two. Flip. The sign. In the middle. So anytime you divide by a negative number or you cross multiply or multiply by a negative number, when you have an inequality, this inequality has to flip. And the other direction. That is the rule that you have to remember. So now I'm going to rewrite this with my new inequality. Excuse me. So I'm going to write negative 5 Y divided by negative 5. I'm going to flip my inequality in the other direction. I had a negative X here, I had a negative 5. In front of this negative X, there's an imaginary one, if you see nothing, put a one there. Plus 20 over negative 5. A negative 5 divided by negative 5 is a one. So I'm left with Y I've already flipped my inequality.
Now I'm going to draw my peace signs. Because. Fraction. Line means division. So really, this is a division line. Really, this is a division line. All the missing are the two dots. So anytime you multiply. Or divide, that is when you draw your peace sign. When you add or subtract, you do, I owe you, and I have to give you. So I'm going to shade in a negative, because I see a negative here. And I'm going to shade in this negative, because I see that negative in front of that number. A negative divided by negative means that this is going to be a positive answer. So here I'm going to write Y with a positive answer. A positive one over 5 X here, you draw my signs plus minus minus. There is nothing in front of the 20. Well, there's a plus sign in front of the 20. So I'm going to shade in the plus sign.
There's a negative sign in front of the 5, so I'm going to shade in the negative side. Which means that this answer is going to be negative. Excuse me. Negative 20 over 5. Remember with fractions, you now have to reduce this fraction. In order to reduce this fraction, I have to use the GCF, the greatest common factor. So I'm going to write out the times tables for 20 and 5 and find the number in their timetables that the biggest. So I have one times 20, two times ten, three times 6 is 18, four times four is 16. So I got to try all the numbers between two and ten. Three four 5. So I have a 5 times four. There are no more numbers between 5 and four, so I'm done. For 5, I have just only a times 5. So do I see a number that's a like, except one. We don't care about one because all multiplication tables have number one in it. I see a 5 here and I see a 5 here.
So this is the GCF. We take that GCF number and we divide it. By the top and the bottom. So 20 divided by 5, 5, divided by 5. So our answer is Y, less than or equal to one over 5 X minus 20 divided by 5. Here, I see 5 times four equals 20. So I see the number 20. I see the number 5. So 20 divided by 5 must be four. Here, 5 divided by 5, I see one times 5 is 5. So I see a 5 here. I see a 5 here. So 5 divided by 5 is one. I don't have to put this one at the bottom of a fraction. Because it's just understood. So why is less than or equal to one over 5 X? But if there's a number one at the top, you have to put that fear. And that's a minus sign. I forgot minus four. So this is our. Slope and Y intercept. Form. So remember in order to graph this, I have to put a dot at negative four and then go up one. And to the right 5. Since this is a positive slope. So let's do that. So I'm going to go back here, make it a little bit smaller. I'm going to put my dot at negative four on the Y axis.
Negative four, I go up one and to the right 5, one, two, three, four, 5, put my dot, and then next thing I do is I determine if this line is dotted or solid, it's going to be solid because there is a equal to sine right up under the inequality. So I already have it as a solid line. My last step is to check and see, do I shade in this side of the line or do I shade in this side of the line? I'm going to try zero zero and see if this point makes the inequality true. If it does, I will shade here. If it doesn't, I will shit on this side. So let's go back to our inequality and let's try to substitute the X with zero in the Y with zero. So here, for Y I'm going to put a zero. I'm just going to have one 5. For the X I'm going to put a zero minus four. Anything times zero is just zero. So actually we have zero, less than or equal to negative four. And we see if this inequality is true.
The PacMan points to whatever is greater. This negative four means I have to give you. $4. This zero means that I. Don't have to give you anything. Would you rather have to give me $4 or would you rather have to give me nothing? You'd rather have to give me nothing. So this inequality should have been pointing towards a zero for it to be true. So actually this inequality is false. It's not true. So that means that I'm not going to shade in the side that contains zero zero because it made it false. So I'll just shade in the other side. And I'm going to hit submit. And that's correct.