Problem 6

Solve for x in terms of a, b, and c from

(a-2*x)/b=(c*x-b*c)/a

and then find x when a=2, b=-1, c=3

Solution

a) Multiply both sides by a*b assuming a*b≠0: a*(a-2*x)=b*(c*x-b*c)

b) Expand both sides: a2-2*a*x=b*c*x-b2*c

c) Collect the x terms: a2+b2*c=x*(b*c+2*a)

d) Solve for x: x=(a2+b2*c)/(2*a+b*c)

e) For a=2, b=-1, c=3:

The numerator is

22+(-1)2⋅3=4+3=7

and the denominator is

2*(2)+(-1)*(3)=4-3=1.

Hence, x=7.

Answer: x=(a2+b2*с)/(2*a+b*c) and for a=2;b=-1;c=3;x=7.