What is (|x-5|)/(|x+2|)<4 ?

The solution to (|x-5|)/(|x+2|) -3/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(|x-5|)/(|x+2|)<4

\frac{∣ x - 5 ∣}{∣ x + 2 ∣} < 4

x < - \frac{13}{3} or x > - \frac{3}{5}

Interval Notation

(- \infty, - \frac{13}{3}) \cup (- \frac{3}{5}, \infty)

Decimal Notation

x < - 4.33333 \dots or x > - 0.6

Solution steps

\frac{∣ x - 5 ∣}{∣ x + 2 ∣} < 4

Find positive and negative intervals

x < - 2, - 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

x < - \frac{13}{3} or - \frac{3}{5} < x < 5 or x \geq 5

Merge Overlapping Intervals

x < - \frac{13}{3} or x > - \frac{3}{5}

x^{2} - 3 x + 2 > 2

x^{2} - 3 x + 2 > 0

∣ 3 x - 2 ∣ > 3 ∣ x - 1 ∣

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 3

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 4

What is (|x-5|)/(|x+2|)<4 ?
The solution to (|x-5|)/(|x+2|)<4 is x<-13/3 \lor x>-3/5