What is |x+2|<4|2x-3| ?

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|x+2|<4|2x-3|

∣ x + 2 ∣ < 4 ∣ 2 x - 3 ∣

x < \frac{10}{9} or x > 2

Interval Notation

(- \infty, \frac{10}{9}) \cup (2, \infty)

Decimal Notation

x < 1.11111 \dots or x > 2

Solution steps

∣ x + 2 ∣ < 4 ∣ 2 x - 3 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

x < - 2 or - 2 \leq x < \frac{10}{9} or x > 2

Merge Overlapping Intervals

x < \frac{10}{9} or x > 2

x^{2} - ∣ x + 2 ∣ + x => 0

∣ 4 - x ∣ < - 11

\frac{( x - 2 )}{( x - 2 )} \cdot (\frac{- 1}{2}) \leq 0

x^{2} - 4 \leq 0

(∣ x ∣ - 5) (∣ x ∣ - 7) \leq 0