|x-1|<2|x|

Solution

∣ x - 1 ∣ < 2 ∣ x ∣

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

Interval Notation

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

Decimal Notation

x < - 1 or x > 0.33333 \dots

Solution steps

∣ x - 1 ∣ < 2 ∣ x ∣

Find positive and negative intervals

x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

x < - 1 or \frac{1}{3} < x < 1 or x \geq 1

Merge Overlapping Intervals

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

20 > 5 (w + 3)

n - 5 < 15

3 x^{2} = - 15

5 x + 13 \geq - 37

\frac{5}{6} - \frac{1}{3}