SOLUTION: 1-(4-3m over 6)= 2m-1 over 5 I am having problem with how to subtract 1 from first term before I cross multiply Jordan

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Question 693756: 1-(4-3m over 6)= 2m-1 over 5
I am having problem with how to subtract 1 from first term before I cross multiply
Jordan
Found 2 solutions by stanbon, RedemptiveMath:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1-(4-3m over 6) = 2m-1 over 5
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1 - (4-3m)/6 = (2m-1)/5
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(6-(4-3m))/6 = (2m-1)/5
--
(2+3m)/6 = (2m-1)/5
-----
Cross-multiply:
10 + 15m = 12m-6
3m = -16
----
m = -16/3 = -5 1/3
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Cheers,
Stan H.
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Answer by RedemptiveMath(80) (Show Source):
You can put this solution on YOUR website!
I'm assuming that "4-3m" is the numerator of the first fraction (in parentheses) and "2m-1" is the numerator of the second fraction. I hope this is the case because I am going to attempt to answer your question with these fractions in mind.

Looking at the core of your problem, we need to be able to change 1 into a fraction with a common denominator between it and the fraction (4-3m)/6. The simplest fraction form of 1 is 1/1, and looking at the denominator of the second fraction, we need to get the denominator of 1/1 to 6. We can multiply by 6 and receive a new fraction of 6/6. Now we can subtract (4-3m)/6 from 6/6 (which is 1):

6/6 - (4-3m)/6
[6-(4-3m)]/6
[6-1(4-3m)]/6
(6-4+3m)/6
(2+3m)/6.

Now we can cross multiply:

(2+3m)/6 = (2m-1)/5
5(2+3m) = 6(2m-1)
10+15m = 12m-6
16 = -3m
m = -16/3.

We can plug what we found for m to check ourselves:
1-(4-3m over 6)= 2m-1 over 5
1-{[4-3(-16/3)]/6} = [2(-16/3)-1]/5
1-[(4+16)/6] = [(-32/3)-1]/5
1 - (20/6) = [(-32/3)-(3/3)]/5
1 - 10/3 = (-35/3)/5
3/3 - 10/3 = (-35/3) * 1/5
-7/3 = -35/15
-7/3 = -7/3.

There is a shortcut method that involves not finding a common denominator. If we have the equation

1-(4-3m)/6 = (2m-1)/5,

We can just multiply EVERY term by the denominator of each fraction. This will eventually get ride of every denominator and help us solve the equation more easily. Let's start with 6:

6(1)-[6(4-3m)/6] = [6(2m-1)]/5
6-(4-3m) = (12m-6)/5.

Now let's do 5:

5(6)-[5(4-3m)] = [5(12m-6)]/5
30-(20-16m) = 12m-6.

Finally, we solve for m:

30-(20-15m) = 12m-6
30-20+15m = 12m-6
10+15m = 12m-6
16 = -3m
m = -16/3.

Be wary of the signs and parentheses. The "-" in front of the parenthetical (4m-3) means that the terms inside of the parentheses are being multiplied by -1. It technically means that this quantity is being subtracted from the numbers in front of it, but this is an easier way of saying it and operating on the equation.