Question

If y=2-3x/x+3 express x in terms of y
[20pts]

Answer 1

a. x = (2 -3y)/(y+3)

b. x = -4/5

Explanation:

a.

Clear the fraction, collect x terms, divide by the coefficient of x.

`y=(2-3x)/(x+3)\\\\y(x+3)=2-3x\\\\3x+xy=2-3y\qquad\text{add $3x-3y$}\\\\x(y+3)=2-3y\qquad\text{factor out x}\\\\\boxed{x=(2-3y)/(y+3)}\qquad\text{divide by the coefficient of x}`

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b.

Put 2 where y is and do the arithmetic.

x = (2 -3(2))/(2 +3) = (2 -6)/5

x = -4/5