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Solve for the unknown, and then check your solution.$$0.4 r-0.52(40-2 r)=100$$

$$755 / 9$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Lectures

00:14

Solve equation, and check …

00:53

Solve each equation.$$…

04:41

Solve for the unknown, and…

06:11

00:37

Check to see if the given …

00:32

Solve each equation. Check…

01:02

Solve the equation. Check …

01:07

Solve each equation, and c…

00:52

Substitute the given value…

01:53

Divide.$$\frac{80 …

05:07

okay for this? A question. We have 0.4 R minus 0.52 times in parentheses for U minus two R is equal to 100. And this is a literary question, because art is raised to the power of one and both of these equations should equal to each other. So we're going to use the fact that addition and subtraction well under each other and multiplication and division will also under each other. And the first thing we have to do is simplified this and we can do this by distributing the 0.52 into the parentheses and to each value here. So we're gonna have negative 0.52 times 40 and also negative 0.52 times negative to our. So let's do that. It's your point for our they were gonna multiply 0.52 times 40 which is gonna be, uh, 20.8. And it's a negative value because the 0.52 is negative. And then we're gonna, um we're gonna add the next values because the negatives cancel each other out. Negative 0.52 times negative two is positive. 1.4 And this one contains the R value and this is equal to 100. So now we're gonna keep simplifying because we could add the R values together. So it's gonna be 0.4 r plus 1.4 r. That's 1.44 are. And then he quit 200. So now we got we want to get rid of this 20.8. And we're gonna do this by adding 20.8 to both sides of the equation. And we're gonna add because 20.8 right here is a negative value and we want to cancel them out. Okay, so now we're gonna be left with 1.44 are the 20.8. Cancel each other out on the right side. They're gonna add up, so it's gonna be 1 20.8. Now we have to divide both sites by 1.44 in order to isolate art. So if we divided by 1.44 we're going to essentially removed this value right here, and we're gonna be left with just are so we're going to divide this by 1.44 and we also divide the right side by 1.44. So now we're left with just 1.44 divided by 1.44. It's just one. So one times are are is equal to 1 20.8, invited by 1.44. So this could be the final answer or could simplify it even further down. For example, um, if we want to get rid of the decimal point, we could just we could either plug this into a calculator and find the fractional form like a more simplified one are. We can multiply both the top and the bottom by 100 in order to remove the decimals. So we multiply the top 500. I'll be 120 80 divided by the bottom 1.424 times 101 144. And we could simplify this even further down by finding what both of these values could be divided by. So you could use a calculator, and it's just gonna be 755 divided by night. So our final our value R is equal to 755 divided by night, and we could collect this back into the original equation to see if it's they're equal to each other. But we have to. Your point. Four times 755 divided by nine minus 0.52 in parentheses. 40 minus good times in parentheses. 755 over nine. So, basically, we want to know if this equals 200 which indeed it does, but we'll just double check with a calculator. So just like these values into your calculator, if possible. 0.52 parentheses. 40 minus two apprentices 755 divided by nine And there we go equals 100 and 100 and details equal 100. So therefore, our our value equals 75 5/9.

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