|x+2|<|2x|

Solution

∣ x + 2 ∣ < ∣ 2 x ∣

x < - \frac{2}{3} or x > 2

Interval Notation

(- \infty, - \frac{2}{3}) \cup (2, \infty)

Decimal Notation

x < - 0.66666 \dots or x > 2

Solution steps

∣ x + 2 ∣ < ∣ 2 x ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - 2 or - 2 \leq x < - \frac{2}{3} or x > 2

Merge Overlapping Intervals

x < - \frac{2}{3} or x > 2

6 x - 8 = 16 + 10 x

\frac{x - 1}{2 x ^{2} - x - 1} \geq 0

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

\frac{x + 1}{x - 1} \leq 4

x - 3 < 5