# Algebra 2, solve with steps

1. Sep 25, 2014

### iamjon.smith

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. Sep 25, 2014

### Ray Vickson

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:
$$\frac{a_1 b_1}{x_1} = \frac{a_2 b_2}{x_2}\, ,\\ \text{so }\; \frac{x_1}{a_1 b_1} = \frac{x_2}{a_2 b_2} \, ,\\ \text{so }\; x_2 = \frac{x_1}{a_1 b_1} a_2 b_2 = \frac{a_2 b_2 x_1}{a_1 b_1}$$