What is 1/(x-3)+1/(3x-21)>= 0 ?

The solution to 1/(x-3)+1/(3x-21)>= 0 is 3 7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/(x-3)+1/(3x-21)>= 0

\frac{1}{x - 3} + \frac{1}{3 x - 21} \geq 0

3 < x \leq 6 or x > 7

Interval Notation

(3, 6] \cup (7, \infty)

Solution steps

\frac{1}{x - 3} + \frac{1}{3 x - 21} \geq 0

Rewrite in standard form

\frac{4 x - 24}{( x - 3 ) ( x - 7 )} \geq 0

Factor

\frac{4 x - 24}{( x - 3 ) ( x - 7 )} : \frac{4 ( x - 6 )}{( x - 3 ) ( x - 7 )}

\frac{4 ( x - 6 )}{( x - 3 ) ( x - 7 )} \geq 0

Divide both sides by

4

\frac{\frac{4 ( x - 6 )}{( x - 3 ) ( x - 7 )}}{4} \geq \frac{0}{4}

Simplify

\frac{x - 6}{( x - 3 ) ( x - 7 )} \geq 0

Identify the intervals

3 < x \leq 6 or x > 7

- 24 x^{2} - 48 x + 360 = 0

\frac{50 x - 3 x ^{2}}{4 π} = 0

2 \cdot \frac{3}{4}

x^{4} + 2 x^{3} + 3 x^{2}

(x + 2) (x - 3) (x + 8) < 0

What is 1/(x-3)+1/(3x-21)>= 0 ?
The solution to 1/(x-3)+1/(3x-21)>= 0 is 3<x<= 6\lor x>7