What is |x-3|<2|x-5| ?

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|x-3|<2|x-5|

∣ x - 3 ∣ < 2 ∣ x - 5 ∣

x < \frac{13}{3} or x > 7

Interval Notation

(- \infty, \frac{13}{3}) \cup (7, \infty)

Decimal Notation

x < 4.33333 \dots or x > 7

Solution steps

∣ x - 3 ∣ < 2 ∣ x - 5 ∣

Find positive and negative intervals

x < 3, 3 \leq x < 5, x \geq 5

Solve the inequality for each interval

x < 3 or 3 \leq x < \frac{13}{3} or x > 7

Merge Overlapping Intervals

x < \frac{13}{3} or x > 7

∣ x + 2 ∣ - ∣ x - 1 ∣ < x

∣ 5 x - 3 ∣ > - 3

d (∣ x - 3 ∣ - 2) > 1

\frac{4 x + 8}{8} > 3

9 ∣ y - 8 ∣ - 6 \geq 30