What is 6/((x-2))<= x-3 ?

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6/((x-2))<= x-3

\frac{6}{( x - 2 )} \leq x - 3

0 \leq x < 2 or x \geq 5

Interval Notation

[0, 2) \cup [5, \infty)

Solution steps

\frac{6}{x - 2} \leq x - 3

Rewrite in standard form

\frac{- x ^{2} + 5 x}{x - 2} \leq 0

Factor

\frac{- x ^{2} + 5 x}{x - 2} : \frac{- x ( x - 5 )}{x - 2}

\frac{- x ( x - 5 )}{x - 2} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x - 5 ) ) ( - 1 )}{x - 2} \geq 0 \cdot (- 1)

Simplify

\frac{x ( x - 5 )}{x - 2} \geq 0

Identify the intervals

0 \leq x < 2 or x \geq 5

- 2 z + 10 + 7 z = 16 z + 7

5 x^{2} + 120 = - 50 x

- 3 = 4 x^{2} - x - 3

1 - 2 x \leq (x + 5)^{2} - 2 (x + 1)

y^{2} - 10 y + 29 = 0