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

$x=8$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

McMaster University

Lectures

01:32

In mathematics, the absolu…

01:11

02:57

In $3-20,$ solve each equa…

05:33

07:29

02:26

01:34

Solve each equation.$$…

01:09

02:46

02:56

Solve and check. $$\frac{3…

03:32

When you have a problem like this, you actually have two different ways that you can choose to solve this out. You can go the normal route that we would use for any rational equation that we want to solve, which would be to find a common denominator and then multiplied by that common denominator to get everything. Um, all our denominators gone, all of them cancelled out, right. However, in the case of this problem, there is another option. Now, this Onley works if you have exactly one fraction on each side of the equation. But if you have only one fraction on each side of the equal sign, this would be something that you can treat like a proportion meaning. If you remember probably a long time ago, when you've done proportions, you are able to cross multiply here, meaning we can set this diagonal of three terrible three of three times X plus two equal to this diagonal of five times X minus two. Again, this is the same thing you would end up getting if you multiplied by a common denominator, right? If you look for a common denominator here, the common denominator between five and three would be to multiply by 15. So if we multiplied, everything here by 15 will think about it. 15 over five out of you put 15 here. 15/5 would cancel 23 right, 15 divided by three for the second fraction would cancel to five. So it works the same way. Either way, you look at it. It really doesn't matter. And I don't know that either one saves you a whole bunch of time. But I didn't want to point out that since there's only one Fraction, one rational expression on each side of the equation, you can just cross multiply. It only works if you have one each side that either way, whichever method you choose to go about, you would end up with where we're here. Three times the quantity of explosive two equals five times the quantity of X minus two. So we would distribute the 33 times X is three x three times to it's six. Then we distribute the 55 times X is five x five times Negative too, is negative. 10. So now our goal is to get all the exes on one side of the equation. Doesn't matter which and get all our constants on one side of the equation. I am going to choose to subtract three X to the other side because I like to keep my ex positive, if possible. And five x minus three X would give me a positive two X. All right. And so then because of that, if I'm gonna put on LAX is on the right side. I need to move that negative 10 over to the left side so that all my constance air on the opposite side. So the opposites attraction is addition. So I would need to add 10 over here, which would give me 16 equals two X. I need to then divide by two to solve out for X. And that would give me that eight is equal to X or X equals eight. Whichever way you prefer to read it.

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