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

The solution to |3x-2|<2|x-4| is -6<x<2

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

∣ 3 x - 2 ∣ < 2 ∣ x - 4 ∣

- 6 < x < 2

Interval Notation

(- 6, 2)

Solution steps

∣ 3 x - 2 ∣ < 2 ∣ x - 4 ∣

Find positive and negative intervals

x < \frac{2}{3}, \frac{2}{3} \leq x < 4, x \geq 4

Solve the inequality for each interval

- 6 < x < \frac{2}{3} or \frac{2}{3} \leq x < 2 or No Solution

Merge Overlapping Intervals

- 6 < x < 2

x^{2} - \frac{7}{2} x + 6

9 (p - q)^{2} + 12 (p^{2} - q^{2}) + 4 (p + q)^{2}

2 x + 8 = - 10

2 x \cdot 2 x

\frac{3}{2} + 3 - 8