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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
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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

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