Algebra

Solving a more complicated equation | Linear equations | Algebra I | Khan Academy

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Let’s try some of the equations a little bit more complicated. Let’s say we have 3 hit x plus 5. Equals 17 So what’s different from that than we have seen in the past The video, suddenly, now we have this plus 5. If only 3x equals 17, you could divide by both sides by 3, and you’d get your answer. But now this 5 seems to spoil things a little. Now, before we even solve that, let’s think What to say. Let’s solve it kind in a concrete way, then we’ll solve Using the processes that we hope to make Feeling after that. So hitting 3 x literally means ………. so let me write it over here. So we have to multiply 3 x. So we literally have x plus x rays add up That is right there 3 x. And then this plus 5, I’m actually writing It is out as the five beings. In addition to 1, 2, 3, 4, 5. And this right here, this x 3 plus 5, is equal to 17. So let me write the equal sign. Now, let me draw 17 objects here. Up to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. Now, these two things are equal, so anything that you do For this side, you need to do to this side. If we get rid of one object here, we might want to get Ditching one object to equalize That is still true. Now, what can we do for both sides of this equation until we are It can be obtained as you used us to where we are It only has 3 x on the left, where We do not have this 5? Well, ideally, we’ll just get rid of this Five objects here. You can literally get rid of these five objects: 1, 2, 3, 4, 5. But, as I said, if the original thing was equal The original thing on the right, if we get rid of five objects from And on the right side, we have to get rid of five objects From the right side. So we have to do it here, too: 1, 2, 3, 4, 5. Now, what is the symbolic method of Acting Taking Far away from five things? Well, you’re subtracting 5 from both sides of this equation. This is what we do here when we took away 5 of Right and right. So we’re subtracting 5 from the left. And that’s what we’ve done here. And I’ve also subtract 5 from the right. This right over there. Now, what is on the left side of the equation Are now? On the right side, you have 5 minus 5. This eliminates. I was just left with 3 x. Various shading of green. Just that you left with 3 x. In negative 5 and cancel. And you can see it here. And when you got rid of these five beings, we were Just left with signs x 3 That’s right here 3 x. The whole reason why we discount 5 is that This 5 wants to go away. Now, what does the left side of the equation look like? Where 3 x will not be – and let me write the equal sign Right under it – equal to newspaper or you can either just Are you an athlete. I say, ok, 17 minus 5. 17 minus 5 is 12. Or you can just count over here. I had 17 things. I took away 5. He left 12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. This is the offering. He just took five things away. So far we have a very clear model. 3 x equals 12. And all we have to do is divide both sides of This equation is 3. So you just left with x on the left side. Since we are dividing – let me choose a nicer color than that. Please let me do this pink. Where you divide the left side by 3, The left side of 3. And remember what is equivalent. And on the left side, any of these things exist anymore, So we should ignore that. None of these things exist anymore. In fact, let me wipe it, as we cannot We might even consider it. And we minus it, so let me clear it. Let me wipe it over here. So now we divide both sides by 3. Divide by the left side 3. In 1, 2, 3. Up to three groups, each containing x. If you divide this left side by 3, you have 1, 2, and 3. So it’s three groups of four. So when you do that mathematically here, 3 Cancel it. 3 times something divided by 3 is just something. So you left with x equal, and then 12 Divided by 3 by 4. You can get x equal to 4, and you can get this setting Same here. When 3 x is divided into three categories, each of Groups have x in it. When you divide 12 into three categories, each group is grouped It has 4 in it, so x must be 4. x equals 4. Let’s do one last time, and this will not direct everything Like this, but hopefully, you’ll see the same type Operations are involved. Let’s tell her – let me just scroll down a little bit. Suppose I have 7 x. So 7x- and I’ll do a little more complicated this time. x 7 minus 2 which is equivalent – it will provide numbers that do not work Nice and clean – 10 negative. And now, suddenly this becomes a lot more than that today you know, We have a negative sign. We have a negative image over here, but we’re going to Do the exact same thing. And the first thing that we want to do if we want to get right Simplified aspect to x 7 just want to get rid For this 2 negative. And what can we add or subtract to both sides of the equation To get rid of this negative 2? Also, if we add 2 to the left side, these two It will cancel players. But remember, this is equal. If we want equality still hold, if we add 2 to The left side, we also have to do it on the left side. So what happens to the new right side that equals? So we only have 7 x, 2 plus 2 negative 0. Can I write to you in addition to 0, or I can just type something in there, And I just write something. And to get 7 x equal to – now, what’s negative 10 plus 2? This is a few reviews to add and Subtract negative numbers. remember. I will draw a number line here for you. If I draw a newspaper number line so this is 9, this is 1. The positive trend can continue. 10 negativity out here. Negative 10, negative 9, negative 8, negative 7. There are a bunch of numbers here. You know, dot, dot, dot. Space doesn’t have to draw them all, but we’ve started 10 negative, and we’re adding 2 to it, so we’re moving in Positive direction on the number of lines. So we’re going 1, 2. So it is 8 negative. Don’t get confused. Do not say, OK, 10 plus 2 is 12, negative until 10 Plus 2 12 negative. No! 10 negative minus 2 would be 12 negative because you had Goes more negative. Here, we have a negative number, but we are Go to the right. We’re going in the positive direction, even this It is 8 negative. So we have 7 x negative 8. Now you can say, too, and how to do it Kind of a problem? You know, I have a negative number here. You can do this exactly the same way. If we want to just have an x \u200b\u200bsign on the left side, we have to Divide by the right side 7, where 7 x is divided by 7, Just cancel 7 off, you left with x. So let’s do that. If you divide by 7, it eliminates those, but you just can’t Do it on the left side. Anything you can do to the left, you must do right For equality is still true. So let’s divide right by 7 as well. And we leave with only equal to x 8 negative divided by 8. We can work it out. It will be some decimal type, if you are to use The calculator, or you can only leave it in the form of a fraction. The negative 8 divided by 7 is the negative 8/7. 8/7 negative, or if you want to write it as a mixed number, x Equals going 7 to 8 once and may remain 1, So the negativity 1 and 1/7. Either one will be acceptable.

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