What is (15-11x)/(x^2-6x+9)<= 1 ?

The solution to (15-11x)/(x^2-6x+9) 3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(15-11x)/(x^2-6x+9)<= 1

\frac{15 - 11 x}{x ^{2} - 6 x + 9} \leq 1

x \leq - 6 or 1 \leq x < 3 or x > 3

Interval Notation

(- \infty, - 6] \cup [1, 3) \cup (3, \infty)

Solution steps

\frac{15 - 11 x}{x ^{2} - 6 x + 9} \leq 1

Rewrite in standard form

\frac{- x ^{2} - 5 x + 6}{x ^{2} - 6 x + 9} \leq 0

Factor

\frac{- x ^{2} - 5 x + 6}{x ^{2} - 6 x + 9} : \frac{- ( x - 1 ) ( x + 6 )}{( x - 3 ) ^{2}}

\frac{- ( x - 1 ) ( x + 6 )}{( x - 3 ) ^{2}} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 1 ) ( x + 6 ) ) ( - 1 )}{( x - 3 ) ^{2}} \geq 0 \cdot (- 1)

Simplify

\frac{( x - 1 ) ( x + 6 )}{( x - 3 ) ^{2}} \geq 0

Identify the intervals

x \leq - 6 or 1 \leq x < 3 or x > 3

n^{2} - 9 n + 8 = 0

18 \cdot \frac{2}{3}

2 x^{2} - 7 x + 3 = 0

(- 2 r^{4} s^{- 3})^{- 2}

(2 x - 12) x = 0

What is (15-11x)/(x^2-6x+9)<= 1 ?
The solution to (15-11x)/(x^2-6x+9)<= 1 is x<=-6\lor 1<= x<3\lor x>3