SOLUTION: 3x/6 -4/12 =7 ; -36x +24=-504 In the following pair of equations, both sides of the equation on the left were multifplied by a number to get the equation on the right. What is

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Question 309282: 3x/6 -4/12 =7 ; -36x +24=-504
In the following pair of equations, both sides of the equation on the left were multifplied by a number to get the equation on the right. What is the number?
I know the answer is -72.
If you could please help me find out how to get that answer that would be so wonderful.
Thank you!!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Well a quick and easy way to get a common multiple of 2 (or more) numbers is to simply multiply them. For instance, a common multiple of 17 and 5 is 17*5=85

In this case, a common multiple between 6 and 12 is 6*12=72. It turns out that the numbers that share the common multiple will go into that common multiple. Ie and . What this means is that you can effectively clear out the denominators of the fractions leaving you with integer terms.

For instance, multiply 72 by to get . In the given problem, the only difference is that 36x is really -36x. So instead we must multiply both sides by -72.

Another quick way to realize that -72 is the magic number is to look at the right side. This side already has an integer which will make life easier for us. Take the number 7 and multiply it by some unknown number 'k' to get 7k. This is now equal to the new right side of -504. Set them equal to get 7k=-504. The task now is to solve the equation 7k=-504. Sure enough, solving the equation will get us k=-72 which is the number we're looking for.