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In $3-20,$ solve each equation and check.$$0.4 x+8=0.5 x$$

$x=80$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

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In mathematics, the absolu…

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In $3-20,$ solve each equa…

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Solve each equation.$$…

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Solve each equation and ch…

If we're trying to solve this equation out for X, then our goal is to get X isolated, meaning get X by itself on one side of the equation. You do have some options on how you can do that. But certainly I see I have two different X terms here. I need to combine those one way or another. So the options are I consider subtract 0.4 X over to the right side, or I can subtract 0.5 X over to the left side. Well, since I know I want to get X by itself, I know that eight will need to be on the opposite side. So I think the best option here would be to subtract 0.4 x to the right side of the equation. Because that way, not only am I combining my exes, but I'm also getting them on the opposite side of eight. Okay, so if I take 0.5 x minus 0.4 x, I'd have just eight over here now and then 0.5 months. 0.4 would be 0.1 x. All right, so that's awesome. Now we are trying to solve for X. We're not trying to solve for 0.1 X, so that means that 0.1 needs to be moved away. Well, it 0.1 times X is what's happening there. The opposite of multiplication is division, so we would want to divide by 0.1. If you take eight divided by 0.1, you get 80 and you just have X on the right side so we'd have ourselves an answer of X equals 80. It looks like if we wanted to check that, then we just go back to the original problem and we plug 80 and forex, so we would have 0.4 times 80 plus eight is equal to 0.5 times 80. All right, that's how you ever If you ever want check a problem that you've sold out, you just take the variable that you are the number that you solved out for. Plug it into the original equation and see if it actually works. So if we take 0.4 times 80 we get 32. So we have 32 plus eight. If we take 0.5 times 80 we get 40 32 plus eight does give us 40 so this problem checks out. Our answer is 80

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