+58 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.
+9481 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 \( -\frac12 \)
