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solving Multi-step equations

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2 Answers

 r + 13   =   1

   12

You have to multiply each side by 12 to get rid of the denominator first because technically the 12 is attached to both the r and the 13

12 ( r + 13) =  (1) 12

        12

r + 13  =  12

   - 13     - 13

r = -1

Comments

First, let me see if I understand the question:

r+13    =    1

------

  12

Assuming I understood your question correctly, here is how I would proceed.

The problem above can also be written:

(r+13)/12 = 1

The / sign means division, which is the same as having a denominator in your fraction. The numerator (or top part of the fraction) is r+13. The denominator is 12.

(r+13)/12 = 1

We want r by itself on one side of the equal sign. Whatever we do to one side of the equal sign, we do to the other.

In this case, start with thing that is outside the parentheses, the 12. It is dividing the r term, so we to move it to the other side of the equal sign, we multiply both sides by 12. (I will use * to mean multiply.)

12*(r+13)/12 = 12*1

(r+13)*12/12 = 12.

(r+13)*12/12 = 12

(r+13) = 12

Multiplying by 12 and dividing by 12 cancel out on the left side. On the right side of the equal sign 12*1 is just 12. We can drop the parentheses on the left because there isn't anything going on besides the 13 being added to r.

r+13 = 12

To move something that is being added to r, subtract it from both sides. In this case, subtract 13 from both sides:

r+13 -13 = 12 -13

r = 12 -13

r = -1

And that is your answer. Adding 13 and subtracting 13 on the left side cancel out, leaving r by itself On the right, we have 12-13 which is -1. So the answer is r=-1.


We check this problem by putting -1 back into the original equation wherever we see r. If we did our work correctly, the answer will make the equation true:

(r+13)/12 = 1

(-1+13)/12 = 1

(12)/12 = 1

12/12 = 1

1 = 1 TRUE, therefore our answer is correct (r = -1).