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how do i find the answer to 3x-12=-2x+83

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2 Answers

When you have the same variable on both sides of the equation you want to start by isolating the variable (in this case x) on one side.
 
I would start by adding 12 to each side
 
3x-12+12=-2x+83+12
 
-12+12 cancels out to zero and you add 12 to 83
 
This leaves you with 3x=-2x+95
 
Next add 2x to each side
3x+2x=-2x+2x+95
 
-2x+2x cancels out to zero
 
This leaves you with 5x=95
 
Now divide each side by 5
 
5x/5=95/5
 
5/5=1 which leaves you with 1x or just x if you prefer. 95/5=19
 
Therefore you answer is x=19
Hope this helps.
The following should help you work towards the answer.
 
1. Let us first put all of the constant terms together. The constants are the numbers without a variable. In this equation they are the -12 and 83.
 
Let us add 12 to the left side of the equation, since -12+12 will equal 0. Of course if we add 12 to the left side, we also need to add 12 to the right side.
 
3x-12=-2x+83
   +12=     +12
3x+0=-2x+95
 
Now the equation is:    3x=-2x+95
 
2. Let us now put the x values together. Above we added 12 since we knew -12+12=0. For the x values I am going to add 2x to the right side, since -2x+2x=0. Of course if we add 2x to the right side, we have to also add 2x to the left side.
 
  3x=-2x+95
+2x=+2x
  5x=0x+95
 
Now the equation is:    5x=95
 
3. Let us "undo" the 5 times x. The equation 5x=95 is a simple way of saying x+x+x+x+x=95, which means that 5 x's will make 95. If I want each x to have an equal piece of 95, then I will have to divide 95 into 5 equal parts. Therefore I will divide 95 by 5.
 
5x=95
5  = 5
x=19
 
4. Check!!! Go back and plug 19 in for the x value and make sure it works.
 
3(19)-12=-2(19)+83
         45=45

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