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In $3-20,$ solve each equation and check.$$\frac{3}{a}+\frac{1}{2}=\frac{11}{5 a}$$

$a=-\frac{8}{5}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

04:04

In $3-20,$ solve each equa…

02:24

Solve each equation.$$…

04:16

02:07

02:17

07:12

01:19

Solve each equation. Check…

04:08

01:10

00:17

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's start with that by subtracting three over a from both sides. And that'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're gonna have 11 over five a minus three a. And now our next step is gonna be to combine. Oh, that'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're gonna do is we're gonna do 1/2 is equal to 11 over five day. Don't. The denominator is already five day, so we don't need to do anything to this one. But for three over a, we'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're going to do is we're going to multiply by five a on both sides because we want our A term on the numerator, not the denominator. What's the best way to do that? To get it out of the denominator by multiplying by. It's reciprocal. So we cancel out the five day and the denominator here in the five that were multiplying by. And let'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's take a look and let'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'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'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'll have to add these to fracture together. 1/2 is the same thing as for eight. We just won'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's take a look at our right hand side or right hand. Side is 11 over five, a 11 over five A's. Let's plug in negative 8/5. So that's gonna be 11 over five times. Negative. 1/5. The fives cancel out, so we'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.

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