Problem

Solve for the specified variable. See Example 12.…

02:17

Problem 50 Hard Difficulty

Solve for the specified variable. See Example 12.
$$
f=7 n(d+d z) \text { for } z
$$

Answer

$\frac{f-7 n d}{7 n d}$

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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

and this problem we're being asked to take the equation. F equals seven n times to quantity of D plus DC We're trying to solve for Z meaning we're trying to isolate Z all by itself. Well, if you know this on the right hand side of our equation, it looks like a distributing problem. So that's exactly what we're going to D'oh! So we're gonna have f equals now. First, we're gonna distribute the seven n two D while seven n times D is equal to seven d n Now the reason why I changed the order of my terms. I typically right, like to write my variables in alphabetical order, but because when you multiply, the order doesn't matter. You could have also written this as seven empty. Now we're gonna multiply seven n times d z Well, seven n times d Z is just plus seven d N z. Now, like I mentioned before, you could have also written this as seven n. D. Z and again because of the view of property. The order we put our variables and doesn't matter as long as you have them all listed. And like I mentioned, I like putting my variables in alphabetical order. But you don't necessarily have to now remember our goals to get dizzy by itself. Well, the first thing is that first term of seven d n is getting added to the term seven D and C So I'm gonna move that to the other side of the equation by subtracting seven d n a from both sides. So what do we have? Well, on the left hand side of the equation, we have f minus seven d n Well, those air not like terms, so we cannot combine them. So we will just be left with F minus seven D at now. On the right hand side, we first have seven d n minus seven d n Well, that would equal zero. So those terms cancel each other out and we're just left with seven d n c. Keep in mind, we're trying to get Z all by itself. So what's happening to see? Well, it's getting multiplied by 70 n. So to get Z by itself, we need to do the opposite of that which would be to divide both sides of our equation by seven D Now on the left hand side, because seven d n does not does not divide evenly into both F and 70 end, we can leave it as it's so. I'm gonna write this over here on the right on the left hand side of the equation will have f minus seven d n a divided by seven D At Now, let's take a look at the right hand hand side of the equation while first says seven divided by seven. Well, that's one. So those will cancel. We have d divided by D also won. So those cancel and then divided by N is also one. So those terms cancel out So no, this we're just left with C And now you've gone and z all by itself. So we've found that f minus seven d n divided by seven d n is equal to Z

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