What is 4/(x-3)<= x+1 ?

The solution to 4/(x-3) = 1+2sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4/(x-3)<= x+1

\frac{4}{x - 3} \leq x + 1

1 - 22 \leq x < 3 or x \geq 1 + 22

Interval Notation

[1 - 22, 3) \cup [1 + 22, \infty)

Decimal Notation

- 1.82842 \dots \leq x < 3 or x \geq 3.82842 \dots

Solution steps

\frac{4}{x - 3} \leq x + 1

Rewrite in standard form

\frac{- x ^{2} + 2 x + 7}{x - 3} \leq 0

Factor

- x^{2} + 2 x + 7 : - (x - 1 - 22) (x - 1 + 22)

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

1 - 22 \leq x < 3 or x \geq 1 + 22

3 a + 2 > \frac{3 a - 6}{3}

x^{2} - 9 = - x^{2} + 9

(\frac{1}{8})^{x - 6} < 4^{4 x + 5}

4 x - 1 < 11

- 58 = 3 x - 5 (2 x - 1)

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