Algebra 2, solve with steps

  • #1
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Homework Statement


[/B]
a1b1/x1= a2b2/x2


solve for x2

Homework Equations



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

The Attempt at a Solution


[/B]
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:

Answers and Replies

  • #2
Ray Vickson
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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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