TenMarks teaches you how to write and solve equations with variables on both sides.
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Learn about Equations with Variables on Both Sides In this lesson, let's learn how we solve equations which have variables on both sides. So as we can see we've got this equation with the variable k exist on both sides. We solved it pretty much the same way. Let me just show you. So here we've got on the right hand side, we've got the number 3 which is multiplied to this expression in parenthesis. So first let's explode that, 3×1 is 3-3×2k is 6k, so on the left hand side I've got 2k-5=3-6k. So since 6k has been subtracted to this side we will add 6k to this side and then we’ll add 6k to this side as well. What do I get? 6k+2k is 8k-5=3, put this and this k is cancelled. So 8k-5=3 as we can see I have to subtract 5. Let’s undo it. So 8k=3+5 is 8. Since k has been multiplied by 8 let's divide by 8. We got 8k/k is k=1. So it looks like the solution for this is k. The solution is k=1. If this is indeed the solution then let's try and substitute it, 2×1 is 2-5 is -3, 3×1-2 is -1×3 is -3, both sides are equal. So solution is k=1. Notice all we did was we exploded this so 2k-5 remain and we distributed 3 to the rest of the equation. And then, since I had 6k and 2k on both sides, the variable on both sides I just move one side to the other. So we added 6k here and here so that we had the variable only on one side. Once we had that 8k –5=3, it’s a regular equation. Let's try and do a word problem that will help us do more like this. It says the long distance rate of two film companies are shown in the table. Company A charges $0.36+$0.30×m for number of minute used. Company B charges $0.60×m for a number of minutes used. It says how long is a call that cost the same amount no matter which company you used? So the total amount for A and B are the same that means A=B or 36+3×m=6×m. It is all in cents, $0.36+$0.30×m=$0.60×m. As we can see variable m is on both sides, here I've got 3m so let's subtract 3m from here and from here, what do I get? 36=6m-3m is 3m or now I've got it looks like m has been multiplied by 3 so let's divide by three on both sides, what do I get? 12=m, so for a 12 minute phone call both would cost the same. Notice all we did is we were given two equations. First one said the cost of plan A is 36+3 times the number of minutes you place the call for. The second one is 6 times per minute so 6×m. So if both calls cost the same then 36×3, 36+3×m $0.36+3 times the number of minutes should be equal to 6 times the number of minutes for the other call or plan and this is equal we just solve to get m = 12, which means for a 12 minute call it would cost the same. Let's prove it. So for a 12 minute call, $0.30 per minute would be $0.36, 36+36 would be $0.72. Here, $0.60 per minute times 12 minute is $0.72. So both calls would cost exactly the same if m=12 or for our 12 minute phone call.