What is |x-2|+|x-1|>1 ?

The solution to |x-2|+|x-1|>1 is x 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

∣ x - 2 ∣ + ∣ x - 1 ∣ > 1

x < 1 or x > 2

Interval Notation

(- \infty, 1) \cup (2, \infty)

Solution steps

∣ x - 2 ∣ + ∣ x - 1 ∣ > 1

Find positive and negative intervals

x < 1, 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

x < 1 or No Solution or x > 2

Merge Overlapping Intervals

x < 1 or x > 2

∣ 2 + 3 x ∣ > 0

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

∣ 4 x - 5 ∣ > 8

\frac{( x + 2 )}{5} < 1

\frac{( x ^{2} - 5 x + 4 )}{( x ^{2} - 4 )} \geq 1