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

i do not understand how to find the answer to the equation above

### 2 Answers by Expert Tutors

Matthew M. | Law Grad Tutors Writing, Test Prep, and More!Law Grad Tutors Writing, Test Prep, and ...
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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.
Rebecca A. | Physics and Math: BeckaPhysics and Math: Becka
4.9 4.9 (13 lesson ratings) (13)
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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