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In $3-20,$ solve each equation and check.$$\frac{7}{2 x-3}=\frac{4}{x}$$

$x=12$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

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Lectures

01:32

In mathematics, the absolu…

01:11

02:57

In $3-20,$ solve each equa…

02:46

01:46

Solve each equation. Check…

02:26

05:33

03:17

01:09

Solve each equation.$$…

02:56

Solve and check. $$\frac{3…

01:28

This is another problem where we have two different options to solve it. We could go about just the general method of finding common denominator, multiply the whole problem by that to cancel out all the denominators. But what I think would be faster in this case, or at least, would be just as fast. I noticed that I have only one fraction on the left side of the equation and one fracture on the right side of the equation. One rational expression on either side. If you have exactly one rational expression, one fraction on either side of the equal son, then you are able to cross multiply here, meaning set this Dagnall of seven times X equal to this Dagnall of four times the quantity of two X minus three. You don't have to do this. You can solve it out the other way of just finding a common denominator. In this case, your common denominator would be X times two X minus three. That would be your common denominator. And if you multiply both sides by that, you're gonna get the same thing that we just got here anyway, So it's truly up to you, but I figured since you know, there are other problems on the section that we're doing with the common denominator. If we're able to cross multiply, I had to show that option as well. We have what we have here. Either way. Seven X equals four times two x minus three is a quantity. We would need to distribute that four for stuff. So four times two X would be a X four times negative three would be negative. 12. My goal is to get all the exes on one side, all the constants on the other side and then isolate X completely. Well, since I already have the minus 12 on the right side, I might as well go ahead and subtract a X to the left. That way that constant gets isolated and the ex gets isolated at the same time. Seven. X minus eight X would be a negative one x or you could just say negative X. You don't have to write the one there, and that is equal to negative 12. Well, if negative X is equal to negative 12 then positive X must be equal to positive 12. So our answer for this would be X equals 12. Now, on this, we do need to do a little bit of checking here because we do have exes in my denominator. So I needed to go to the original equation. Just gonna rewrite it over here. Seven over two X minus three equals four over X. And what we're gonna do is we're going to plug 12 in for both of those exes and make sure that we don't accidentally get zero in either of the denominators, because then it would turn out This is actually a no solution problem. Undefined. So that means we would have 7/2 times 12. My history equals four over 12. Well, two times 12 is 24 so we'd have 24 minus three. And over here, I've got nothing to do with that. 24 miles three is 21 so we've got 7/21 is equal to 4/12. Neither of those air zeros. So this is looking good. I just need to simplify those fractions. 7/21 simplifies to 1/3 4/12 also simplifies toe 1/3. So this checks out. I did not get zero in my denominator. Didn't get undefined or anything. So my answer truly is 12

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