in-3-20-solve-each-equation-and-check-04-x805-x

Question

In $3-20,$ solve each equation and check.
$$
0.4 x+8=0.5 x
$$

Derrick Hanson · Accepted Answer

If we&#x27;re trying to solve this equation out for X, then our goal is to get X isolated, meaning get X by itself on one side of the equation. You do have some options on how you can do that. But certainly I see I have two different X terms here. I need to combine those one way or another. So the options are I consider subtract 0.4 X over to the right side, or I can subtract 0.5 X over to the left side. Well, since I know I want to get X by itself, I know that eight will need to be on the opposite side. So I think the best option here would be to subtract 0.4 x to the right side of the equation. Because that way, not only am I combining my exes, but I&#x27;m also getting them on the opposite side of eight. Okay, so if I take 0.5 x minus 0.4 x, I&#x27;d have just eight over here now and then 0.5 months. 0.4 would be 0.1 x. All right, so that&#x27;s awesome. Now we are trying to solve for X. We&#x27;re not trying to solve for 0.1 X, so that means that 0.1 needs to be moved away. Well, it 0.1 times X is what&#x27;s happening there. The opposite of multiplication is division, so we would want to divide by 0.1. If you take eight divided by 0.1, you get 80 and you just have X on the right side so we&#x27;d have ourselves an answer of X equals 80. It looks like if we wanted to check that, then we just go back to the original problem and we plug 80 and forex, so we would have 0.4 times 80 plus eight is equal to 0.5 times 80. All right, that&#x27;s how you ever If you ever want check a problem that you&#x27;ve sold out, you just take the variable that you are the number that you solved out for. Plug it into the original equation and see if it actually works. So if we take 0.4 times 80 we get 32. So we have 32 plus eight. If we take 0.5 times 80 we get 40 32 plus eight does give us 40 so this problem checks out. Our answer is 80

Dilip Paruchuri · Answer

Okay. Hey, guys. So in this problem, we&#x27;re given the equation 3/4 x equals 14 minus X and were asked to solve this for X. And then after we saw this for ex worker and actually verified that it&#x27;s true, because when you have an equation, it&#x27;s really easy to verify. An answer is true, because you just plug it in back into the equation and see if both sides are equal. So first, let&#x27;s start off by solving this equations. We have 34 Sex equals 14 minus X, so we want to get all our exes on one side, and all are constants on one side. So in order to get all our exes on one side, let&#x27;s add X to both sides. When we add X to both sides, we get the re Ford&#x27;s X Plus X, which is seven forts X equal to 14 because these X&#x27;s cancel out over here and now we have 7/4 X equals 2 14 In order to isolate this X, we&#x27;re gonna need to multiply by 4/7 on both sides when multiplying by four sevens on both sides on the left side, we get cancellation, and so on the left side. We&#x27;re just left with X equals and on the right side we do 14 times 4/7. And before we just instead of just multiplying out, um, 14 times four, divided by seven. We could reduce our terms here. We know that 14 7 goes into 14 twice, so we could, ah, simplify and we have two times for and we get Our X is equal to eight. And so let&#x27;s verify this is the left hand side. Just so most label like this left hand side we have. So it&#x27;s bugging three Fords X. Our ex, we said, is equal to eight. So 3/4 of eight hopes reports of eight is equal to Let&#x27;s call Simplify. Four goes into twice, so 3/4 of eight is equal to six. And now let&#x27;s take a look at our right hand side. Our right hand side is 14 minus X. We set our X was eight 14 minus eight is equal to six. We see that both our left hand side and our right hand side or equal so we know that our solution is correct. And so our final answer is X equals eight. Thanks for listening eyes. And I hope this helped answer this equation

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we have the rational equation X over experts. Five equals 2/3. Now, the first step in this problem is to make it easier for us for solve this by a kn fraction ing everything so we don&#x27;t want we don&#x27;t really want to deal with the fraction. So what we&#x27;re gonna do is we&#x27;re gonna first multiply by X plus five on both sides of the equation. So first step, we&#x27;re gonna multiply by expose five on the left hand side, and we&#x27;re gonna most by by experts five on the right hand side. So on the left hand side of the to expose fives here, cancel out and we&#x27;re left with X on the left hand side. When the rights hand side, we&#x27;re left with 2/3 times X plus five. And now, in order to make things a little bit more easier for ourselves, what we can do is we can cross multiply, not cross month by, but in a sense, divide out the 2/3 from the right hand side. So we&#x27;re just left with the X plus five. So what we&#x27;re gonna do is we&#x27;re going to multiply by three halves on the right hand side and three halves on the left hand side. The goal of this basically this step right here is just so we could make this equation just little bit easier to solve. Make out, make the algebra nicer for us. And so what happens on the right hand side is the 2/3 cancels out with it that we have so on the left hand side, you&#x27;re just left with experts five, which is nice, which is really nice to work with. And on the left hand side, you&#x27;re left with the rehabs times X, which is also a nice basically a nice function to work with. And so we want to get all our variables to one side now. So let&#x27;s subtract X on both sides, tracking acts on both sides. We get 1/2 X equals five and in order to get her ex by itself, we&#x27;ve multiplied by two on the left hand side and two on the right hand side. Then we get that X is equal to 10. Now we plug in, shrug and see whether the left hand side equals the right hand side. We have our left hand side is equal to X over explode. Oh, that&#x27;s right. That better is equal to X over X plus five. We plug in our value of 10. So we have 10 over templates. Five at 10 over. Tempus five is the same thing as 10 over 15 which is the same thing as 2/3. And as you noticed, our right hand side is also equal to 2/3. So we know that our left inside right to inside are equal. So value X equals 10 is the correct solution for this equation, and we have verified it. So thanks for listening, guys. And I hope this help solve this rational.

Derrick Hanson · Answer

When you have a problem like this, you actually have two different ways that you can choose to solve this out. You can go the normal route that we would use for any rational equation that we want to solve, which would be to find a common denominator and then multiplied by that common denominator to get everything. Um, all our denominators gone, all of them cancelled out, right. However, in the case of this problem, there is another option. Now, this Onley works if you have exactly one fraction on each side of the equation. But if you have only one fraction on each side of the equal sign, this would be something that you can treat like a proportion meaning. If you remember probably a long time ago, when you&#x27;ve done proportions, you are able to cross multiply here, meaning we can set this diagonal of three terrible three of three times X plus two equal to this diagonal of five times X minus two. Again, this is the same thing you would end up getting if you multiplied by a common denominator, right? If you look for a common denominator here, the common denominator between five and three would be to multiply by 15. So if we multiplied, everything here by 15 will think about it. 15 over five out of you put 15 here. 15/5 would cancel 23 right, 15 divided by three for the second fraction would cancel to five. So it works the same way. Either way, you look at it. It really doesn&#x27;t matter. And I don&#x27;t know that either one saves you a whole bunch of time. But I didn&#x27;t want to point out that since there&#x27;s only one Fraction, one rational expression on each side of the equation, you can just cross multiply. It only works if you have one each side that either way, whichever method you choose to go about, you would end up with where we&#x27;re here. Three times the quantity of explosive two equals five times the quantity of X minus two. So we would distribute the 33 times X is three x three times to it&#x27;s six. Then we distribute the 55 times X is five x five times Negative too, is negative. 10. So now our goal is to get all the exes on one side of the equation. Doesn&#x27;t matter which and get all our constants on one side of the equation. I am going to choose to subtract three X to the other side because I like to keep my ex positive, if possible. And five x minus three X would give me a positive two X. All right. And so then because of that, if I&#x27;m gonna put on LAX is on the right side. I need to move that negative 10 over to the left side so that all my constance air on the opposite side. So the opposites attraction is addition. So I would need to add 10 over here, which would give me 16 equals two X. I need to then divide by two to solve out for X. And that would give me that eight is equal to X or X equals eight. Whichever way you prefer to read it.

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we&#x27;re given the equation X minus 0.5 X equals 19 and like the previous problems were asked to solve for a value of X and verify that it&#x27;s correct by plugging it back in and checking if the left hand side, right hand side are equal. So let&#x27;s get started. So we have our left side is X minus 0.5 times X. And our goal right here is to isolate the ex Soto. We have our X multiplied by some constant or just our X. So in this case, we can&#x27;t just solve for our ex. So let&#x27;s try to go for X just multiplied by a constant. In order to do that, we can just factor out our X on the left hand side and we get one minus 0.5 equals 19 are one minus 0.5 is just a constant. And if we simplify, that one minus 0.5 is equal to 0.95 X equals 19. Now we have a decimal on the left hand side and normally are the are decimals just a constant Normally you just divide out by 0.95 on both sides. But in reality, dividing by a decimal is computational. Really, it&#x27;s not the easiest. So what I normally would like to do is convert our decimal into a fraction. We know 0.95 is equal to. So we have 0.95 is our desperate. We know that that&#x27;s equal to 95 over 100. And if we simplify this a little bit further, we see that if we divide five on the numerator and the denominator 95 over 100 is equal to 19 over 20 so 0.95 X is the same thing as in 19 over 20 X. Now we have 19 over 20 X is equal to 19. And if we just divide out the 19 over 20 on boats sides, we can clearly and easily get our answer by just crossing up by canceling the 19 and the cancer. In the 20 over 19 here we get X is equal to 20. That&#x27;s our chance. That&#x27;s what we think are answers to this equation. And so let&#x27;s check it on the right hand side. We already know that are right hand side is equal to 19. So let&#x27;s take a look at our left hand side. Our left hand side says we have X minus your 0.5 x and we know that we can just plug in our value for 20 to verify. We get 20 minus 0.5 times 20 is equal to. So we know our 20 is just a 20. And now if we if we take a look at our 0.5 times 20 we can see if we do the same steps like we did above here, we see that are 0.5 is equal to five over 100 which is equal to one over 20. Just simple tricks to help you solve your problem a little bit easier. So we have won over 21. Substitute that in and then we get 20 minus one over 20 times 20. That&#x27;s equal to 20 minus one. That&#x27;s equal to 19. These two things the left hand side, right hand side of equal. So we know our answer. X equals 20 is correct. And that is the correct answer for this problem. So thanks for listening, guys. And I hope this helps

Derrick Hanson · Answer

So we&#x27;re trying to solve this problem for X first thing notice here is that obviously we do have some rational expressions here. Some fractions. I don&#x27;t want to leave those those fractions. So the first thing I want to do is I want to find a common denominator so that I can multiply the entire problem by that number to get rid of all of my denominators. Right now, I see a denominator of three and denominator of four. So the question is, what is the least what is the lowest number that both three and four can multiply up to? In this case, I would say that is 12. Okay, so we&#x27;re going to multiply this entire problem then by 12. Understand? This is 12/1, meaning 12 is being multiplied to the numerator. Okay, I have to multiply every single part of the equation by 12 so that I&#x27;m not actually changing the value of this equation. Meaning I&#x27;m going to take 12 times two x over three. Well, 12 times two x would be 24 x over three. Then I have to take 12 times one pretty straightforward. 12 times one is just 12 right, And then finally, I have to take 12 times three x over 4 12 times three x would be 36 x over four. So now, assuming that we chose something that a number that truly was a common denominator, all of my fraction should be able to reduce well. 24 x over three could reduce down to eight. X 12 Doesn&#x27;t need to reduce its on a fraction anyways. And 36 x over four should reduce to nine x 36 divided by four is nine so good? Looks like we did do the right thing here We did pick a common denominator cause all my fractions are gone. So now I simply just need to solve this equation out to get X by itself and figure out what happens equal. Ah, I would say they use this way to do that would be dis attract eight x to the right side because that goes ahead and isolates the Constance as well as the exes at the same time. So that would leave me with just 12 on the left side of the equation. Nine X minus eight X would be one x or just x so looks like our answers. X equals 12. That&#x27;s it.

Problem

In $3-20,$ solve each equation and check. $$ 0.…

Problem 9 Easy Difficulty

In $3-20,$ solve each equation and check.
$$
0.4 x+8=0.5 x
$$

Answer

$x=80$

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$x=80$

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Ann Xavier Gantert

Algebra 2 and Trigonometry