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

$a=20$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Oregon State University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

03:45

In $3-20,$ solve each equa…

03:06

04:00

03:17

02:57

02:24

02:26

05:33

07:29

01:13

Solve each equation, and c…

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've done is that instead of variable X were being given a variable, eh? But that really doesn't matter. It's not gonna change the way we solve this equation. So let's get started. First, we want to isolate all the eight terms to one side of the equation. So what I'm gonna do is I'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'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's little Alva. Frankly, I find out dividing my decimals quite annoying. So we're gonna convert that into a fraction really quickly because it'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're left with a and on the right hand side that the res simplify out, cancel out, and we're left with 20. So our answer is a equals 20. So let'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'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'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're left with one over 20 times 20 plus three one over 20 times twenties, one So we'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're equal to each other. So a equals 20 is our correct answer. Thanks for listening, everyone. And I hope this hoped

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