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In $3-20,$ solve each equation and check.$$\frac{3}{4} x=14-x$$

$x=8$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 7

Solving Rational Equations

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Campbell University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

03:32

In $3-20,$ solve each equa…

02:26

05:33

02:57

03:17

01:27

Solve each equation and ch…

02:24

01:09

Solve each equation.$$…

02:56

Solve and check. $$\frac{3…

Okay. Hey, guys. So in this problem, we're given the equation 3/4 x equals 14 minus X and were asked to solve this for X. And then after we saw this for ex worker and actually verified that it's true, because when you have an equation, it's really easy to verify. An answer is true, because you just plug it in back into the equation and see if both sides are equal. So first, let's start off by solving this equations. We have 34 Sex equals 14 minus X, so we want to get all our exes on one side, and all are constants on one side. So in order to get all our exes on one side, let's add X to both sides. When we add X to both sides, we get the re Ford's X Plus X, which is seven forts X equal to 14 because these X's cancel out over here and now we have 7/4 X equals 2 14 In order to isolate this X, we're gonna need to multiply by 4/7 on both sides when multiplying by four sevens on both sides on the left side, we get cancellation, and so on the left side. We're just left with X equals and on the right side we do 14 times 4/7. And before we just instead of just multiplying out, um, 14 times four, divided by seven. We could reduce our terms here. We know that 14 7 goes into 14 twice, so we could, ah, simplify and we have two times for and we get Our X is equal to eight. And so let's verify this is the left hand side. Just so most label like this left hand side we have. So it's bugging three Fords X. Our ex, we said, is equal to eight. So 3/4 of eight hopes reports of eight is equal to Let's call Simplify. Four goes into twice, so 3/4 of eight is equal to six. And now let's take a look at our right hand side. Our right hand side is 14 minus X. We set our X was eight 14 minus eight is equal to six. We see that both our left hand side and our right hand side or equal so we know that our solution is correct. And so our final answer is X equals eight. Thanks for listening eyes. And I hope this helped answer this equation

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