in-3-20-solve-each-equation-and-check-02-a005-a3

Question

In $3-20,$ solve each equation and check.
$$
0.2 a=0.05 a+3
$$

Dilip Paruchuri · Accepted Answer

Hey, guys. So in this problem, we have the equation. Zero point you A is equal to 0.5 a plus three. Ah, The difference between this equation and the previous equations that we&#x27;ve done is that instead of variable X were being given a variable, eh? But that really doesn&#x27;t matter. It&#x27;s not gonna change the way we solve this equation. So let&#x27;s get started. First, we want to isolate all the eight terms to one side of the equation. So what I&#x27;m gonna do is I&#x27;m going to subtract 0105 a from both sides of the equation. So we have all our eight terms on the left hand side of the equation. So we do this and the 0.5 minus Europe wants your five A. This cancels out here point to minus 0.5 is equal to 0.15 a share, A 0.158 So we&#x27;re left with 0.15 days equal to three. And so we have a decimal here. Normally, we just divide out by 0.15 That&#x27;s little Alva. Frankly, I find out dividing my decimals quite annoying. So we&#x27;re gonna convert that into a fraction really quickly because it&#x27;s so much easier to divide up by fractions, 0.15 is equal to 15 over 100 divide five on the new moran and the denominator. And then you get the Rio over 20 three over. So we substitute three over 20 in for a 0.153 over 20 times A is equal to three. Now we just divide by three over 20 on both sides, and we just reciprocal it to get 20 over three on the left inside and 20 over three of the right hand side. And so we know that 20 over three times three over 20 is just one. So on the left hand side, we&#x27;re left with a and on the right hand side that the res simplify out, cancel out, and we&#x27;re left with 20. So our answer is a equals 20. So let&#x27;s verify that left hand side is gonna be equal to zero point to a Is there a 0.2 times 20 0.2? If it&#x27;s right, that better start to read 0.2 times 20 0.2. If we read it as a fraction is 2/10 at times 20. If we do that, the 10 goes into 22 times. So that cancels and we&#x27;re left with two times too. So are left hand side is equal to four. Right hand side is equal to 0.5 a plus three. If we plug in 20 we get 0.5 times 20 plus three and 0.5 We ride as a fraction is one over 20. Just following the same process, we did hear it over 100 divided by five on boats on newer and a dominator. And so we&#x27;re left with one over 20 times 20 plus three one over 20 times twenties, one So we&#x27;re left with one plus three and we get the right hand. Side is equal to four. Left hand side is equal to four. They&#x27;re equal to each other. So a equals 20 is our correct answer. Thanks for listening, everyone. And I hope this hoped

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

we&#x27;re solving for be here. So our goal is to try and get be by itself on either side of the equation. Doesn&#x27;t matter which, in this case it truly doesn&#x27;t matter, because I can see I&#x27;ve got two different terms with a B, so I&#x27;ll need to combine those somehow. But I can also see that I have a constant on either side of the equation. So no matter which direction you choose to go, it&#x27;s going to take multiple steps to get both, um, my Constance on one side and my B value combined on the other side. When it doesn&#x27;t matter which direction you go, I usually prefer to have my variable on the left. Plus, In this case, it is a negative 0.5 B, which means I would be adding 0.5 b to the other side. So that means I also get to keep things positive. I&#x27;ll skip to keep my be term positive, which I like to do is well, if possible. So that was my preference again. You could totally choose to subtract one point to be to the right side. It&#x27;s not gonna mess your answer up it would still completely work. This is just my preference. So 1.2 b plus 0.5 b would be 1.25 B. Then we have the minus three that were just rewriting. And it&#x27;s equal to seven, all right, trying to get be by itself. So that means I can&#x27;t allow that minus three to stay with it. Well, the opposite of subtraction is addition, so my next step would be to add three to the other side. Giving us 1.25 B is equal to 10 grand. Seven plus three is 10. And now, finally, I have 1.25 times B. I need that 1.25 to go away, while the opposite of multiplication is division. So I would be dividing by 1.25 cancels out on the left side. And my answer is, whatever 10 divided by 1.25 happens to be. If you do 10 divided by 1.25 you will see that it gives you eight as your answer. If you want to check that, simply go back up to the original equation and plug in eight everywhere you CB and then see if you get a true statement. Meaning you would have 1.2 times eight minus three on the left side of the equation and you would have seven minus 0.5 times eight on the right side of the equation. Well, if you take 1.25 Sorry. 1.2 times eight. You would get 9.6 minus three if you take 0.5 times eight, you get 0.4 9.6 minus three gives us 6.6 seven, minus 0.4. Also gives us 6.6. So that&#x27;s a true statement. Does problem checks out our answers? A.

Dilip Paruchuri · Answer

Hey, guys. So in this equation, we have three over a plus. 1/2 is equal to 11 or five. A. Our first step is to bring all of our is gonna be to bring all of our A terms to one side of the equation. So let&#x27;s start with that by subtracting three over a from both sides. And that&#x27;s gonna give us on our left hand side just 1/2 because of three over Ace, cancel out and our right hand side we&#x27;re gonna have 11 over five a minus three a. And now our next step is gonna be to combine. Oh, that&#x27;s an A, by the way in on eight and A our next step is gonna be combining these 28 terms in tow. One a term. So I want to do that by finding a common denominator or common denominator here is clearly five, eh? So what we&#x27;re gonna do is we&#x27;re gonna do 1/2 is equal to 11 over five day. Don&#x27;t. The denominator is already five day, so we don&#x27;t need to do anything to this one. But for three over a, we&#x27;re gonna multiply by five on the numerator and the denominator and get 15 over five A if you know where. Five. A And so we have the equation supervised toe 1/2 and we know that 11 11 05 a minus 50 or five a is minus for over five day. And now what we&#x27;re going to do is we&#x27;re going to multiply by five a on both sides because we want our A term on the numerator, not the denominator. What&#x27;s the best way to do that? To get it out of the denominator by multiplying by. It&#x27;s reciprocal. So we cancel out the five day and the denominator here in the five that were multiplying by. And let&#x27;s finish this form of here. And so on the left hand side will lift with fi A over to is equal to minus four. And now, if we want to buy buy 2/5 on both sides, we get that our answer to this is gonna be a is equal soon. Negative. Eight. It Yeah, And so now let&#x27;s take a look and let&#x27;s verify it for both The bar, for both of the spokes sides of our equation left hand side first. So we had three over a plus 1/2 three over. A is gonna be such A is going to substitute it in for 1/5. So we&#x27;ll have three divided by 8/5 plus 1/2 and three divided by negative. 8 50 is the same as three times negative. Five over eight Just how you divide fractions and that&#x27;s gonna be plus 1/2 native. 33 times. Notify Will Rate is the same. His negative 15 over eight and our 1/2. Since we know that, we&#x27;ll have to add these to fracture together. 1/2 is the same thing as for eight. We just won&#x27;t buy Buy four on both sides of the equation. That gives us a negative 11 over eight on our right on our left hand side. Sorry, so they could have 11 over eight is water left hand side equals tomb. And now let&#x27;s take a look at our right hand side or right hand. Side is 11 over five, a 11 over five A&#x27;s. Let&#x27;s plug in negative 8/5. So that&#x27;s gonna be 11 over five times. Negative. 1/5. The fives cancel out, so we&#x27;re left with 11 over negative. 11 over eight his right hand side left inside are equal. So we know that a equals negative 8/5 is our answer and it is correct. Thanks for listening. And I hope this hoped with solving this ration.

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 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.

Problem

In $3-20,$ solve each equation and check. $$ 1.…

Problem 10 Hard Difficulty

In $3-20,$ solve each equation and check.
$$
0.2 a=0.05 a+3
$$

Answer

$a=20$

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$a=20$

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Ann Xavier Gantert

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