What is (3x-1)/(|x-1|)>= 4 ?

The solution to (3x-1)/(|x-1|)>= 4 is 1/3 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(3x-1)/(|x-1|)>= 4

\frac{3 x - 1}{∣ x - 1 ∣} \geq 4

\frac{1}{3} \leq x < 1 or x > 1

Interval Notation

[\frac{1}{3}, 1) \cup (1, \infty)

Decimal Notation

0.33333 \dots \leq x < 1 or x > 1

Solution steps

\frac{3 x - 1}{∣ x - 1 ∣} \geq 4

Move

4

to the left side

\frac{3 x - 1}{∣ x - 1 ∣} - 4 \geq 0

∣ x - 1 ∣ \geq 0

\frac{a}{b} \geq 0 and b \geq 0

then

a \geq 0 and b > 0

3 x - 1 \geq 0 and ∣ x - 1 ∣ > 0

3 x - 1 \geq 0 : x \geq \frac{1}{3}

∣ x - 1 ∣ > 0 : x < 1 or x > 1

Combine the intervals

x \geq \frac{1}{3} and (x < 1 or x > 1)

Merge Overlapping Intervals

\frac{1}{3} \leq x < 1 or x > 1

14 x = 10

x^{6} + c^{2} x^{4} + c^{4} x^{2} + c^{6}

3 s^{4} t + 3 s^{3} t - 6 s^{2} t

7 x = 4

2 x + 4 \leq 5

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