What is (-2x+4)/(3x-9)<= (x+5)/(3x-9) ?

The solution to (-2x+4)/(3x-9) 3

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(-2x+4)/(3x-9)<= (x+5)/(3x-9)

\frac{- 2 x + 4}{3 x - 9} \leq \frac{x + 5}{3 x - 9}

x \leq - \frac{1}{3} or x > 3

Interval Notation

(- \infty, - \frac{1}{3}] \cup (3, \infty)

Decimal Notation

x \leq - 0.33333 \dots or x > 3

Solution steps

\frac{- 2 x + 4}{3 x - 9} \leq \frac{x + 5}{3 x - 9}

Rewrite in standard form

\frac{- 3 x - 1}{3 x - 9} \leq 0

Factor

\frac{- 3 x - 1}{3 x - 9} : \frac{- 3 x - 1}{3 ( x - 3 )}

\frac{- 3 x - 1}{3 ( x - 3 )} \leq 0

Multiply both sides by

3

\frac{3 ( - 3 x - 1 )}{3 ( x - 3 )} \leq 0 \cdot 3

Simplify

\frac{- 3 x - 1}{x - 3} \leq 0

Identify the intervals

x \leq - \frac{1}{3} or x > 3

x^{2} - 3 x - 18 > 0

- 2 n \leq - 12

\frac{2}{3} (6 x - 5) = 2 - \frac{1}{3} (3 x - 2)

y^{- 1}

- \frac{1}{2 x ^{\frac{3}{2}}}

What is (-2x+4)/(3x-9)<= (x+5)/(3x-9) ?
The solution to (-2x+4)/(3x-9)<= (x+5)/(3x-9) is x<=-1/3 \lor x>3