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Homework Help: Algebra 2, solve with steps

  1. Sep 25, 2014 #1
    1. The problem statement, all variables and given/known data

    a1b1/x1= a2b2/x2

    solve for x2

    2. Relevant equations

    no relevant questions apply, this is a stand alone review question

    3. The attempt at a solution

    multiply times reciprocal to get rid of denominator on left

    (x1) (a1b1/x1)= (a2b2/x2)(x1)

    a1b1 = (a2b2x1/x2)

    multiply times reciprocal to get rid of denominator on right

    (x2) a1b1/x1= a2b2x1/x2 (x2)

    a1b1x2 = a2b2x1

    divide by a1b1 to get x2 alone

    a1b1x2/a1b1 = a2a2x1/(a1b1)

    x2 = a2b2x1/(a1b1)

    I know I have missed something, but this is my best attempt at solving this problem. Could someone please review and help me figure out what I missed?
    Last edited: Sep 25, 2014
  2. jcsd
  3. Sep 25, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You have not missed anything; your answer is correct (provided that you never divide by zero anywhere, so provided that all x's a's and b's are nonzero). Your argument is very long-winded, though, and can be shortened into two lines:
    [tex] \frac{a_1 b_1}{x_1} = \frac{a_2 b_2}{x_2}\, ,\\
    \text{so }\; \frac{x_1}{a_1 b_1} = \frac{x_2}{a_2 b_2} \, ,\\
    \text{so }\; x_2 = \frac{x_1}{a_1 b_1} a_2 b_2 = \frac{a_2 b_2 x_1}{a_1 b_1} [/tex]
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