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Solve for the unknown, and then check your solution.$$\frac{3}{5} y-\frac{3}{4}=\frac{1}{4} y+\frac{7}{10}$$

$$2977$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Oregon State University

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Idaho State University

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Okay, so we have to follow in. Linear Equation, which is 3/5 times Y minus 3/4, is equal to 1/4 times Y plus 7/10. So this is a linear equation, because our unknown value that we're looking for is raised to the power of one. So it's zero y, and both of these expressions should equal to each other, and we're gonna use the fact that addition and subtraction will under each other, Multiplication and division will also under each other. So first thing we're gonna try to do is simplify this equation. And what we want to know is that when we're adding fractions, assuming we don't converted to decimals, we're just where we want to add them and give them the common denominator. So, for example, with the white values, they don't have the same common denominators. So we're gonna have to find a common denominator between these two fractions, and that's between five and four. And the common denominator would be 20. So in order to get 24 3 or five, we're gonna have to multiply both the top and the bottom by four. So it's gonna be four times three divided by five times four. In order to get 20 on the denominator on, then we'll do the same thing on the right side. Where were y value so well? First do that. We'll try to get the values into a common denominator on. We'll do the same thing with these numerical values. Three or four and 7/10 off. I am common denominator for those. So first we'll do the white value. So the common denominator is 20 and we have to multiply five by four in order to get there. So we multiply top and bottom by four. So there's three times 43 times towards just 12, divided by 20. And why, minus our 3/4, then one or four. In order to get it to 20 we have to multiply the top in the bottom by five. So it's gonna be one. Times five is just five divided by four times five. That's 20 and then plus seven, the better by time. So now we have to find common denominator toward these two fractions without the white value. So between four and 10, a common denominator is 20 so we'll just write down the same thing again. 12 Divide every 20 times Y minus our Fraction three or four. But now we're going to multiply by five the top and the bottom in order to get it to 20. So three times five is 15 divided by four times five with just 20. This is equal to our five. Divided by 20. That's why Value? Yeah, plus seven divided by 10. So this is we're gonna look to play the top and the bottom by two in order to get the same common denominator of 20. So it's gonna be 14, or sometimes two is 14 about a very clean. And now we can rearrange the equation in order to add, uh, the white values together and just the numerical values together. So we're gonna move the 5/20 times. Why? To the left side of the equation. We're going to do that by subtracting five or 20 times. Why? To both sides of the equation. So we're gonna have we're gonna have minus 5/20 10 20 until both sides of the equation minus 5, 20 times. Why? Okay, Now the five or 20 times why is going to cancel on the right side and on the left side is gonna be 12 or 20 times y minus five or 20 times y. So, since they have the same common denominator weaken, subtract there at them and which is going to subtract enumerators and keep the denominator the same. So it's gonna be told, minus five, a seven. 7/20. I'm quite we'll keep it in parentheses to show that it's a fraction in reality fractions or just division minus 15 divided by 20. Since it's equally true again, the five or 20 y value is gonna it's gonna cancel out. Now we're gonna have 14/20 school. So now what we want to do with this equation, we wanna move this 15/20 value to the right side of the equation. We're going to do that by adding 15/22 both sides, so we're gonna add 15 or 20 in order to cancel it out on the left side and moved to the right side. So and that's going to cause them to cancel out on the website because it's gonna, um, out of 20 And this is gonna equal so it's gonna be 14 plus 15. That's 29 on. Then remember that the denominator stays the same one we're adding or subtracting fractions. So now we have this value, so in over 20 times, why is equal to 29/20? And now we're just going to simply multiply by the inverse of 7/20 to isolate our white value. It's gonna be 20 divided by seven and same thing on the other side. We're gonna bye bye, 22 vertebrae. Seven our 24 7 inches saying the inverse of seven. Number 20. So this is gonna cancel loud to 17 or 20 times 24 7 is just one. So we're left with simply just why? Why is equal to 29 times 20 over 20 times seven. So we see that 20 is both on the numerator and the denominator, so they're going to cancel out each other. Um, we're left with simply just 29/7. Yes. So our Y value is equal to 29 divided by seven. Yes, and I will just like this into a calculator to see if that's correct or not so well, just replaced a three. Uh, any white values in the beginning, with simply 29/7, we have drew for five times 29 or seven Sorry runs through over four. It's equal to one or four, and our value, which is 29 or seven, please 1007 over 10. So if you were to put like these numbers into a calculator just as the way it is very simple, you should get one point roughly 1.73 This is just, um, this is wrong. Rounded up 1.73 equals to 1.73 Again, it's just estimate the number is a lot longer, but basically they're both the same 1.73 and therefore our Y value equals 29 divided by seven hopes.

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