What is (6-2y)/y >= y-3 ?

The solution to (6-2y)/y >= y-3 is y<=-2\lor 0<y<= 3

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(6-2y)/y >= y-3

\frac{6 - 2 y}{y} \geq y - 3

y \leq - 2 or 0 < y \leq 3

Interval Notation

(- \infty, - 2] \cup (0, 3]

Solution steps

\frac{6 - 2 y}{y} \geq y - 3

Rewrite in standard form

\frac{6 + y - y ^{2}}{y} \geq 0

Factor

\frac{6 + y - y ^{2}}{y} : \frac{- ( y + 2 ) ( y - 3 )}{y}

\frac{- ( y + 2 ) ( y - 3 )}{y} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( y + 2 ) ( y - 3 ) ) ( - 1 )}{y} \leq 0 \cdot (- 1)

Simplify

\frac{( y + 2 ) ( y - 3 )}{y} \leq 0

Identify the intervals

y \leq - 2 or 0 < y \leq 3

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