en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

| 1/(x-2)|<4

Solution

\frac{1}{x - 2} < 4

Solution

x < \frac{7}{4} or x > \frac{9}{4}

+2

Interval Notation

(- \infty, \frac{7}{4}) \cup (\frac{9}{4}, \infty)

Decimal Notation

x < 1.75 or x > 2.25

Solution steps

\frac{1}{x - 2} < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < \frac{1}{x - 2} < 4

\frac{1}{x - 2} > - 4 and \frac{1}{x - 2} < 4

(x < \frac{7}{4} or x > 2) and (x < 2 or x > \frac{9}{4})

Merge Overlapping Intervals

x < \frac{7}{4} or x > \frac{9}{4}

Popular Examples

|x-5|+|x+4|<= 7

∣ x - 5 ∣ + ∣ x + 4 ∣ \leq 7

|x-1|-|x-2|+|x+1|>|x+2|+|x|-3

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x + 1 ∣ > ∣ x + 2 ∣ + ∣ x ∣ - 3

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

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

|((3x))/(2+5)|<= 2

\frac{( 3 x )}{2 + 5} \leq 2

|((x+4))/((x+2))|<= 1

\frac{( x + 4 )}{( x + 2 )} \leq 1

Frequently Asked Questions (FAQ)

What is | 1/(x-2)|<4 ?
The solution to | 1/(x-2)|<4 is x< 7/4 \lor x> 9/4