What is |3x+1|>= 2|x-6| ?

The solution to |3x+1|>= 2|x-6| is x = 11/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

|3x+1|>= 2|x-6|

∣ 3 x + 1 ∣ \geq 2 ∣ x - 6 ∣

x \leq - 13 or x \geq \frac{11}{5}

Interval Notation

(- \infty, - 13] \cup [\frac{11}{5}, \infty)

Decimal Notation

x \leq - 13 or x \geq 2.2

Solution steps

∣ 3 x + 1 ∣ \geq 2 ∣ x - 6 ∣

Find positive and negative intervals

x < - \frac{1}{3}, - \frac{1}{3} \leq x < 6, x \geq 6

Solve the inequality for each interval

x \leq - 13 or \frac{11}{5} \leq x < 6 or x \geq 6

Merge Overlapping Intervals

x \leq - 13 or x \geq \frac{11}{5}

∣ 2 x + 8 ∣ - 6 = - 12

\frac{4 3}{2}

x^{5} + 8 x^{2}

5 - 8 x = 2

What is |3x+1|>= 2|x-6| ?
The solution to |3x+1|>= 2|x-6| is x<=-13\lor x>= 11/5