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Step-by-step Solution of Equation in One Variable

Date: 05/13/98 at 01:25:36
From: Alicia
Subject: Linear equations. Formula please!

I have been working at this problem:

   2 - 2(w + 6) = 2(w + 5)

The answer sheet says the answer should be -5, but I've gotten all 
kinds of weird answers. I think I'm just misusing the formula, so 
could you show me every little step to solving this problem?

Thank you for your time,
Alicia


Date: 05/13/98 at 10:54:14
From: Doctor Rob
Subject: Re: Linear equations. Formula please!

Use all the laws of arithmetic:

   the Commutative Law of Addition (CLA)
   the Commutative Law of Multiplication (CLM)
   the Associative Law of Addition (ALA)
   the Associative Law of Multiplication (ALM)
   the Distributive Law (DL)
   and the properties of negatives and zero, of reciprocals and one,
      and of equality.

     2 - 2*(w + 6) = 2*(w + 5)          given problem
   2 - (2*w + 2*6) = 2*w + 2*5          by the DL
  2 + (- 2*w - 12) = 2*w + 10           by prop. of - and arith. facts
   -2*w + (2 - 12) = 2*w + 10           by ALA and CLA
         -2*w - 10 = 2*w + 10           by prop. of - and arith. facts
    2*w - 2*w - 10 = 2*w + 2*w + 10     by adding 2*w, by prop. of =
    w*(2 - 2) - 10 = w*(2 + 2) + 10     by the ALA, CLA, and DL
          w*0 - 10 = 4*w + 10           by prop. of - and arith. facts
            0 - 10 = 4*w + 10           by the prop. of 0
               -10 = 4*w + 10           by the prop. of 0
          -10 - 10 = (4*w + 10) - 10    by adding -10, by prop. of =
               -20 = 4*w + (10 - 10)    by ALA and arith. facts
               -20 = 4*w + 0            by prop. of -
               -20 = 4*w                by prop. of 0
             -20/4 = 4*w/4              by dividing by 4 and prop of =
                -5 = (4/4)*w            by ALM, CLM and arith. facts
                -5 = 1*w                by prop. of reciprocals
                -5 = w                  by prop. of 1
                 w = -5                 by prop. of =

-Doctor Rob, The Math Forum
Check out our web site! http://mathforum.org/dr.math/

Associated Topics:
Middle School Algebra
Middle School Equations

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