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Solve for the unknown, and then check your solution.$$3 p+2(5 p-6)=19+4(7-2 p)$$

$$59 / 21$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

Campbell University

Baylor University

Lectures

00:54

Solve each equation, and c…

01:19

02:08

01:21

Solve each equation.$$…

00:34

01:27

Solve for the indicated va…

03:13

01:55

03:33

Solve equation, and check …

All right, so we have the following linear equation three times p plus two times in parentheses. Five p minus six is equal to 19 plus four tense in parentheses, seven minus two Pete. So these air two expressions that were supposed to equal to each other and it's a linear question because they're p is raised to the power of one. We're gonna turn itself for P. And we're going to do this by knowing the fact that addition and subtraction under each other and multiplication and division under each other. So first thing we're gonna do is simplify this equation and we're gonna have to distribute the two and the four onto each number here. So on the left side, we're gonna have two times five p and then also two times negative six on the right side, we're going to distribute the 4 to 7 and the four to negative two p. So we're gonna have three p both two times five p, which is just 10 p Again. That's because two times five is 10 minus two times six, which is 12 and then on the right program. Frankie, let's distribute. Afford to the to this parent disease four times seven, which is 28. It is four times two p, which is just eight peak. So now we can simplify this further by adding, um, by adding like value. So we're gonna have three p plus. 10 p will be at it, and on the right side, 19 plus 28 can be at it. So three p plus 10 piece just 13 p minus 12. That's equal to 19 plus 28. Actually, that's equal to 47 finance eight people. And now we're going to rearrange this equation so that we get the P values on the left side and just any numerical values with a P on the right side. So we're going to do this by adding eight p to both sides of the equation because we want to get the the peace to the left side. Speed Pete, That's 13 People's eight p is 21 people minus 12 equals 47 then the eight piece cancel each other out. Now we want to move the negative talk to the right tight, and we're gonna do that by adding plus 12 and then on the right side will be plus 12. So now the twelves cancel each other out on the left side. We have 47 plus 12, which is 59. Now, we want to get this p value by itself, because we want to figure out what it is. So we're gonna have to take the 21 times p get rid of the 21 by dividing it by 21. So we take this value 21 times p divided all by 21. Then divide the right side also like 21. So now we have on the left side 21 divided by 21 is just one. So we just we're left with just p or one Time to pee is equal to 39 divided by 21. Well, this is our answer 50 59 divided by 21. And we can double check with a calculator to see if this is correct or not by simply plugging in our P value back into the equation, which was three times p, which was replaced P with 59 divided by 21. So we have three times 59 the better by 21 plus two, then five times Latina in the very by 21 and then six. Right then this is equal to 19. Those four time seven minus two 59 divided by 21. I'll just move this over a little bit to the left and again we'll just plug these values into a calculator both the left side and the right side, and we should end up with a value. So three times. 59 divided by 21 plus two times five times 59 divided by 21 minus six. So it's going to be a bit messy if we just plug them all in. But we should end up with 24.52 roughly estimate on both sides of the equation, and therefore, Pete indeed does equal 59 divided by 21.

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