For \(y=\frac{1-x}{2x+3}\)and \(x\neq-\frac{3}{2}\), what is the value of \(y\) that is not attainable? Express your answer as a common fraction.

Williamjwu8
Apr 30, 2017

#1**+2 **

Solve the equation for x, and then set the denominator = 0. Whatever y value makes the denominator = 0 is not attainable.

y = \(\frac{1-x}{2x+3}\) Multiply both sides by (2x + 3)

y(2x + 3) = 1 - x Distribute

2xy + 3y = 1 - x Add x to both sides.

2xy + 3y + x = 1 Subtract 3y from both sides.

2xy + x = 1 - 3y Factor out an x on the left side.

x(2y + 1) = 1 - 3y Divide both sides by 2y + 1

x = \(\frac{1-3y}{2y+1}\)

Now set the denominator = 0 and solve for y.

2y + 1 = 0

2y = -1

y = \( -\frac12 \)

Therefore, the value of y that is not attainable is \( -\frac12 \)

hectictar
Apr 30, 2017