en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

|(3-x)/(x-4)|<= 2

Solution

\frac{3 - x}{x - 4} \leq 2

Solution

x \leq \frac{11}{3} or x \geq 5

+2

Interval Notation

(- \infty, \frac{11}{3}] \cup [5, \infty)

Decimal Notation

x \leq 3.66666 \dots or x \geq 5

Solution steps

\frac{3 - x}{x - 4} \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq \frac{3 - x}{x - 4} \leq 2

\frac{3 - x}{x - 4} \geq - 2 and \frac{3 - x}{x - 4} \leq 2

(x < 4 or x \geq 5) and (x \leq \frac{11}{3} or x > 4)

Merge Overlapping Intervals

x \leq \frac{11}{3} or x \geq 5

Popular Examples

h + 1.5 = 8.4

simplify 5/2*8/20 simplify

\frac{5}{2} \cdot \frac{8}{20}

simplify 4/(2i)simplify

\frac{4}{2 i}

simplify sqrt(2*5)simplify

2 \cdot 5

6(x^2+1)-(2x-4)(3x+2)<= 3(5x+21)

6 (x^{2} + 1) - (2 x - 4) (3 x + 2) \leq 3 (5 x + 21)

Frequently Asked Questions (FAQ)

What is |(3-x)/(x-4)|<= 2 ?
The solution to |(3-x)/(x-4)|<= 2 is x<= 11/3 \lor x>= 5