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Solve for the unknown, and then check your solution.$$\frac{3}{4} w+2=w-\frac{1}{2}$$

$$10$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

McMaster University

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okay for this lingering question, we have the following 3/4 times W plus two equals W minus 1/2. So this is a linear equation because they'll be used raised to the power of one, and both expressions are going to equal each other. So when you use the fact that addition and subtraction willing to each other and multiplication and division will under each other first step we have to simplify. So there is no simplifying here, but we do have to rearrange the equation a bit in order to move the ws around. So we want to get we would want to get this w this three or four w to the right side of the equation and then move this half to the left side of the equation. So in order to do that, we have to first subtract, um, subtract 3/4 times w onto both sides of the equation. So is three or four. Then we're gonna be left with the three or four w minus three or four W cancels each other out. So we're just left with two equals. Where were you? Minus three or four? Minus have. But you can either keep the fractions infraction form or turn it into decimal form, which is a lot easier. Uh, this is basically just gonna be this w over here is one. Or you could look at it as for divided by four if we want to keep it in just correcting for him. So in order to simplify this, this is gonna be 4/4, minus three or four. So we're gonna subtract, since they have a common denominator, for we're just going to subtract the numerator, which is four minus three. So in this case, that's gonna be four Ministries one and then the denominator stays the same before, so we're gonna be left with two equals, one divided by four or 1/4. The real again. If we did, we did. We did it in decimal form. It would have just been one minus 10.75 which is 0.25 a little bit quicker, but we'll keep it infraction for him for now and again. This is minus 1/2. And we want to get rid of this 1/2. And we'll do that by adding one over to to both sides of the equation. Not over here. The same thing. Two plus went over to so on the right side that won over two. So cancel each other out. And then now we have two plus 1/2. So to we want to get it to come in the nominator with two. So we could either do the same thing, keep it in for action for him, or convert this fraction to decimal, which is a lot easier, but let's just keep it infraction form for now. So in order to add them all together, they need to have the common denominator right now to is just simply to over one. And in order to get the common denominator of to, I'm gonna have to multiply both the top and the bottom of to by two. So that's going to be four are simply for divided by two for over two. Let's have is equal to 1/4 w Now we could add these up together and again the they have a common common denominator. So we grabbed him up, which is that the new the numerator, which is gonna be four plus one that's five by two by two. This is equal to one divided by four or 1/4 things W Now we want to isolate the w. So do this by most of playing the inverse of 1/4, and the inverse of 1/4 is just 4/1. So we're going to multiply four divided by one, which is simply just four one. Multiply the right side of the equation, the left side of the equation. Also by four. Now we're going to have I've already two things for that's five times four that's 2020 divided by two is equal to the one or four times for over one cancels each other out is equal to W. And we could simplify this further, and we'll see that 20 develop. It is just 10, then equals W or simply w equals 10. So we could plug 10 back into the original equation to see if, if that's true or not, and we'll see we have three divided by four or three or four. Thanks, Stan was true. Is equal to turn minus half or one or two. So on the left side we have 3/4 times 10/1. So this is three times 10. That's 30. 30 divided by four plus two is equal to and many have We're gonna have Thio convert the 10 into a common. Then we're gonna have to get a 10 to common denominator off, too, because right now it's 10 divided by one so the common denominator will be to in order to get that would have to multiply the top and bottom by two. So that's two times 10 and two times one. So that's 20 over to in this half. Oh, and we call the convert this to we'll have to convert this to in order to add it with 30/4 with, um Well, we're gonna have to multiply the top and bottom of 2/1 with four song. Let me just go right over here to make a more simple with the right top and bottom by four. So that's gonna be eight invited by four now. Well, at the top in the bottom. I mean, we'll add the tops only and keep the bottoms the same. So it's gonna be 30 because eight that's 38 divided by four or 38/4. This equal to 20 minus one does 19, and then we'll keep denominated the same. We can see that if we simplify 30/4 and equals 19 over to because 38 divided by two, is 19 and for the better way to is to mhm. I'm sorry to read here, so therefore w equals 10.

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