What is |3x+1|<2|x-6| ?

The solution to |3x+1|<2|x-6| is -13<x< 11/5

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|3x+1|<2|x-6|

∣ 3 x + 1 ∣ < 2 ∣ x - 6 ∣

- 13 < x < \frac{11}{5}

Interval Notation

(- 13, \frac{11}{5})

Decimal Notation

- 13 < x < 2.2

Solution steps

∣ 3 x + 1 ∣ < 2 ∣ x - 6 ∣

Find positive and negative intervals

x < - \frac{1}{3}, - \frac{1}{3} \leq x < 6, x \geq 6

Solve the inequality for each interval

- 13 < x < - \frac{1}{3} or - \frac{1}{3} \leq x < \frac{11}{5} or No Solution

Merge Overlapping Intervals

- 13 < x < \frac{11}{5}

\frac{1}{x} + \frac{1}{x + 1} < \frac{2}{x + 8}

2 w y + 3 y x - 8 w z - 12 z x

- 2 b^{2} + 5 ab + 7 a^{2}

2 4^{\frac{1}{2}}

18 r^{3} t^{2} + 12 r^{2} t^{2} - 6 r^{2} t