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

Question

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

Answer 1

I would use the zero product principle,

3x--2x - 12 + 83 = 0

5X = 95

X= 19

Answer 2

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.

Answer 3

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