Problem

Solve for the specified variable. See Example 12.…

02:47

Problem 51 Hard Difficulty

Solve for the specified variable. See Example 12.
$$
G=g(4 r-1) \text { for } r
$$

Answer

$$r=\frac{G+g}{4 g}$$

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Precalculus

Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 4

Formulas

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Video Transcript

we're being asked to take the equation. Capital G equals lower case. G times to quantity of four are minus one and we're being asked to solve for our In other words, we want to get our all by itself. Well, if you know, this on the right hand side is just a distributing problem. So what we're going to do is distribute the G to both terms in that parentheses, E So we'll still have capital G equals while g times for our is just four g r. Then we need to multiply g times. Negative one. Well, that is simply just negative, G. Now remember, we're trying to get our by itself. Well, the term four g r is gonna subtracted by lower case G. So to move that lower case G to the other side, I'm going to add it to both sides of my equation. So on the left hand side, we have capital G plus a lower case G, which means they are not like terms, so we cannot combine them so we'll simply be left with capital G plus lower case G Well equals what? We didn't do anything to that for gr term so I'm simply going to bring it down. And then we had negative G plus ci. Well, that's equal to zero. So they cancel each other up. Now, remember, we're trying to get our by itself. Well, what's happening to our well, it's getting multiplied by four times G. So to get rid of it, we need to do the opposite. In other words, we're gonna divide both sides of our equation by four G Now, on the left hand side of our equation. Because we can't divide both capital G and little G by four G evenly, we can leave it as is. So I'm gonna go over here to the right. So on the left hand side of our equation will have capital G plus a lower case G all divided by four times lower Case G is equal to while on the right hand side No, this we have four divided by four, which is one so they cancel and G divided by G is also one. So those also canceled. So know this. We're just left with our and now we've got an r all by itself. So what with sounds is that capital G plus lower case G all divided by four times lower Case G is equal to our

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