Problem

Solve each equation, if possible. $$ \frac{2}{5} …

02:17

Problem 85 Hard Difficulty

Solve each equation, if possible.
$$
\frac{2}{3} y+2=\frac{1}{5}+y
$$

Answer

$\frac{27}{5}$

Related Courses

Precalculus

Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 2

More about Solving Equations

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Video Transcript

So, like decimals, fractions give people a little bit of a hard time. So our goal usually is to just zap those fractions right out of the way. Because why deal with them If we could deal with real indicators? If there's a strategy to just deal with those investors, let's use it. So I'm Inna Multiply. This is a very funky looking five. Okay, so I am trying to clear out my denominators, and I'm gonna do that by looking for the LCD or the least common denominator. So I'm asking, what is the LCD or the least common denominator for three and five? And that number, the smallest number they go into is 15. So I'm gonna multiply everything by 15. Okay? What that will do is when I distributed here, the 15 and the three are going to simplify. I've simplified to five, so I will have five times, two times why or 10? Why here? There's nothing to simplify. So I just have 30 on the right. I'm gonna do the same logic. So 15 times 1/5 while 1/5 of 15 is three. And here again, nothing to simplify. So I just have 15 why and now there are no fractions. It's less intimidating for people. It's just a simple, straightforward to step equation. So I'm going to subtract three to get my integers on the left and I get 10 y plus 27 equals 15. Why, Then I'm gonna want my variables on the right to the opposite side. So I will subtract 10 white, undo it, and I get 27 equals five. Why? Which means to get why I divide by five and I end up with y equals 27 5th not the prettiest number, but that's okay. We're gonna plug it in to check that this works. So I'll just plug in 27 5th everywhere I see a why and I'm trying to see Is this indeed equal to 1/5 times 27 5th Okay, let's go ahead and simplify here. So two times 27 is 54 3 times 55 is 15 plus two. I'm gonna go ahead and put this in terms of 15. So that's 45th and I'm gonna go ahead and add these. So is that the same as 28 5th? Okay, since these are like denominators Let's add them together. I have 84 15th plus 28. Excuse me equals 28 5th That's what I'm trying to check. And since I'd like to see if they're actually the same, I'm seeing that 15 divided by three is five. So let's just divide the top and bottom by three. When you divide 84 by three take a guess what magical number you get? Yes, it is 28 when you divide 15 by three, you get five. So this is indeed correct. And why is 27 5th?

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