Problem

Solve for the specified variable. See Example 12.…

03:06

Problem 49 Hard Difficulty

Solve for the specified variable. See Example 12.
$$
T=4 b(a+a m) \text { for } m
$$

Answer

$$m=\frac{T-4 a b}{4 a b}$$

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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 for being asked to take the equation t equals four b times the quantity of a plus a. M. We're being asked to solve for em. So in other words we're trying to isolate are variable of em. Well, let's think about what we can do here. Well, on the right hand side of the equation, it looks like we have a distributing problem. So let's go ahead and distribute the four B to both of the terms in the parentheses, so we're gonna have t equals first. We need to multiply four b times a well four B times A is equal to four a. B. Now you could have also said it's for be a because remember the order and rich you multiply does not matter. I typically wait to write my variables in alphabetical order, though next we need to multiply for B times eight times out. Well, for B times, A M will be equal to positive four a. B. And just like I mentioned before, I typically like to write my terms in alphabetical order. But if you have written for B A M, that would also be to say Okay, well, Now we've gone over the bar. Parentheses Keep in mind We're trying to get em all by itself. Will know this right now we're adding for a B to the term for a B. M. So I first need to move that for a B to the other side. To do that, I'm going to subtract for a B from both sides of our equation. Now, on the left hand side, we have t minus for a B. Well, because they're not, like terms, we simply will have just t minus for a B on the right hand side of the equation. We first have four a B minus for a B. Well, that would equal to zero. So these two terms cancel each other out, and we will simply be left with four a b. M. Now remember, we're still trying to get done by itself. Well, what's happening? Toe em in this case? Well, it's getting multiplied by four ap. So to get them by itself, we're going to do the opposite. Meaning we're gonna divide both sides of our equation by for a B. So now if we look on the left hand side of our equation, because we can't divide for a be evenly So both terms of tea and for a b weaken simply rewrite this. I'm gonna come right over here to the right as t minus four ap, divided by four a beam. Now, on the right hand side of that equation, know this. We have four divided by four, which is one. So those will cancel a divided by A, which is also one. So those cancel and be divided by B is also one, So they cancel up. So no, those were just left with them. And now we've gone and em all by itself. So what we found is that t minus four AP all divided by for a B is equal to m.

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