What is |x-3x^2|<|1-3x| ?

The solution to |x-3x^2|<|1-3x| is -1<x< 1/3 \lor 1/3 <x<1

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|x-3x^2|<|1-3x|

x - 3 x^{2} < ∣ 1 - 3 x ∣

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

Interval Notation

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

Decimal Notation

- 1 < x < 0.33333 \dots or 0.33333 \dots < x < 1

Solution steps

x - 3 x^{2} < ∣ 1 - 3 x ∣

Find positive and negative intervals

x < 0, 0 \leq x \leq \frac{1}{3}, x > \frac{1}{3}

Solve the inequality for each interval

- 1 < x < 0 or 0 \leq x < \frac{1}{3} or \frac{1}{3} < x < 1

Merge Overlapping Intervals

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

246 = 77 + 13 x

u^{2} - 9 u - 2 u + 18

60 = \frac{3}{4} h

(- 3 v)^{5}

5 c = - 35

What is |x-3x^2|<|1-3x| ?
The solution to |x-3x^2|<|1-3x| is -1<x< 1/3 \lor 1/3 <x<1