Pallavi K. answered • 10/03/13
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Personalized, versatile tutoring: enthusiastic Duke grad (BSc)
The prompt asks you to rewrite the equation to solve for the variable of interest, that is the variable you're asked to solve for (e.g. "t" in problem number 1).
What does this mean in practice? Basically, you want to get the variable of interest on one side of the equals sign, and everything else on the other side.
I'll provide a simple example first so that you understand the concept behind what you have to do, and then walk you through the two problems.
Example problem
2 + 5 = 7
Solve for "5". In other words, put this equation in terms of "5".
"Simple", you say. "I know that 7 - 2 = 5, so 5 = 7 - 2". Great! Now how did you arrive at your answer?
This is what this exercise of rewriting equations is really about---showing that you know how to get to your answer, not the answer itself.
So let's break down the steps in solving for "5":
Given: 2 + 5 = 7
Okay, so you're asked to get "5" on one side and everything else on the other side of the equals sign. Let's choose have "5" on the left side for this example (it is convention to have the variable you're solving for on the left-hand side of the equation (i.e. to the left of the equals sign)).
Our first move is to bring "2" to the right-hand side of the equation. How do we do that? Well, when we want to "move" a number or variable across the equals sign, we must either add or subtract that term from both sides of the equation. This is important---anytime you perform an operation (e.g. subtraction, addition) on one side of the equation, you must do the same thing to the other side of the equation.
So what does that look like? To get "rid" of the "2" from the left side and bring it to the right side, we must subtract 2 from both sides:
2 + 5 - 2= 7 - 2
You see how on the left side we can rearrange the numbers to read: (2+ -2) + 5 ? The stuff in the parentheses equals zero! Great. So now we have:
0 + 5 = 7 -2
which we can rewrite as:
5 = 7 - 2
Hopefully why I did what I did made sense. If not, the reason why I bothered to show you the steps involved in 2 + 5 = 7 will hopefully become clear when you go through the two problems that were given to you.
Now let's look at your first problem: Solve for t in the equation: -9 = t + 4s.
Let's apply the same reasoning and method to solving for "t" that we used in solving for "5".
Given: -9 = t + 4s
1. Bring "t" to the left side. How do we do that? We have to subtract "t" from both sides. Why? This would make the right side to read: (t + -t) + 4s.
-9 - t = t + 4s + -t
which is the same as
-9 - t = 4s + (t + -t)
which reduces to
-9 - t = 4s
2. We're still not done. We want "t" alone on the left side and we have a pesky "-9" hanging out with our "t" that wants to be left alone. So what do we do? The same concept! We want to add 9 to both sides this time to make the left side read (-9 + 9) - t (because that is the same as 0 + t, which is the same as having t alone)!
-9 - t + 9 = 4s + 9
which is the same as
(-9 + 9) - t = 4s + 9
which is the same as
-t = 4s + 9.
3. Almost done! One last thing to do because we have "-t" but we want "t". So if we multiply the left side by "-1" we'll get t. But remember, if you do an operation on one side of the equation, you have to do it to the other side as well!
-t * -1 = (4s + 9) * -1
t = -4s + -9
Voila! You have "t" on the left side, all alone as we wanted, and it equals -4s - 9. Yay!
Now I think you can do your second problem on your on. Try it out first on your own, and if you get stuck, read through the example and the first problem to figure out what to do, and then see if you get the same answer I got (which I have written below).
Given: B = 5/7(A - 11)
1. B * (7/5) = (7/5) * (5/7)(A - 11)
2. (7/5)B = A - 11
3. (7/5)B + 11= A - 11 + 11
4. (7/5)B + 11 = A
Answer: (NO PEEKING!!!) A = (7/5)B + 11
