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Kathye P. | Math Geek, passionate about teachingMath Geek, passionate about teaching
5.0 5.0 (150 lesson ratings) (150)

Hi, Samantha.

To solve an equation, you want to "undo" what is being done to the variable. The -12y means -12 times y (when you have a letter and a number, you don't need to write the multiplication sign.)

To undo multiplication, we divide. And we have to do the same thing to both sides of the equation to keep them equal. So, we are going to divide both sides of the equation by -12 (I am using the / to show division):

30 / -12 = -12y / -12

30 divided by -12 is -2.5

-12y divided by -12 is    1y,  which can also be written as    y      so we get:

-2.5 = y

If you plug -2.5 back into the original equation to check it, you get:

30 = -12 * -2.5       (the asterisk stands for the multiplication symbol)

The multiplication works, so your answer is   y = -2.5

You could also leave it as a mixed number, -2  1/2


Hope this helps!



Helga M. | Lots of Experienc: 20 years College Teaching, 35 years TutoringLots of Experienc: 20 years College Teac...

Solving linear equations:  How do I solve 30=-12y?

One way to solve linear equations is to view the equation like a balance for weights where the equal sign is the fulcrum and your job is to always keep the balance even. To keep a balance even, you always need to do the same thing to both sides of the balance.

  • If you remove half of the left side, you need to remove half of the right side
  • If you add 3 to the left side, you need to add 3 to the right side
  • if you triple the left side, you need to triple the right side
  • etc.

To know what to do to the balance, you look to the variable. The variable is "wrapped like a present" according to the order of operations.

Example: 3x + 4 = 13

1.    Look only at the side with the variable and understand how it is wrapped according to the order of operations

To get 3x + 4, x was "wrapped" by

    • first multiplying with 3  (multiplication before addition)
    • then adding 4

2.    To solve the equation, you need to "unwrap" in the reverse order and you need to do exactly the same thing to both sides

  • Start with your equation:  3x + 4 = 13
  • Reverse the last step by doing the opposite, here it is to subtract 4, on both sides of the equation to keep it balanced. You get:   3x + 4 - 4 = 13 - 4
  • Simplify: the unwrapping step will cancel out the wrapping, here + 4 - 4 cancels and you get
                                                     3x = 9
  • Reverse the next step by doing the opposite: here it is to divide by 3, on both sides of the equation to keep it balanced. You get   3x/3 = 9/3
  • Simplify: the unwrapping step will cancel out the wrapping, here the 3s cancel and you get
                                                    x = 3

In your example
                                30  =  - 12y
the y is wrapped by being multipied with -12. Since the opposite of multiplying is dividing, you need to divide by -12. Again, you will need to do it to both sides. You get

                               30/-12 = -12y/-12

Simplify by dividing the numbers or reducing the fraction as required by your problem. on the right side, the -12 cancels out again and 30/-12 reduces to -5/2. You get

                             -5/2 = y

If you like the keeping both sides balanced approach, I will be happy to explain how it works for all kinds of linear equations. Just send me an email.

Caroline A. | Dedicated To Success: English, Science, Math, & Beyond!Dedicated To Success: English, Science, ...
4.7 4.7 (137 lesson ratings) (137)


In this problem your goal is to get "y" by itself. Right now the -12 is attached to y. To get rid of it you have to do the opposite operation (opposite operations: if its addition use subtraction, if its multiplication use division) There is an imaginary multiplicatio sign between -12 and y thats whats holding it together so it looks like this 30=(-12)(y)


so all you have to do is divide both sides by -12

30/-12 = -12y/-12

30 divided by -12=2.5  -12y/-12= y (the -12's cancel)

you are left with : 2.5=y

Jose R. | AcademicTutor ProficiencyAcademicTutor Proficiency

Hello Samantha


Every time you have an equation the answer will be y=a number.

This problem 30 you dont nothing to conbine like terms.

In the other side of the equation -12y are Multiple. You always do the opposite of Multiple is divide by the same number and sign to absolate the variable.