What is |3x-2|>3|x-1| ?

The solution to |3x-2|>3|x-1| is x> 5/6

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|3x-2|>3|x-1|

∣ 3 x - 2 ∣ > 3 ∣ x - 1 ∣

x > \frac{5}{6}

Interval Notation

(\frac{5}{6}, \infty)

Decimal Notation

x > 0.83333 \dots

Solution steps

∣ 3 x - 2 ∣ > 3 ∣ x - 1 ∣

Find positive and negative intervals

x < \frac{2}{3}, \frac{2}{3} \leq x < 1, x \geq 1

Solve the inequality for each interval

No Solution or \frac{5}{6} < x < 1 or x \geq 1

Merge Overlapping Intervals

x > \frac{5}{6}

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 3

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 4

\frac{2}{∣ x - 2 ∣} > \frac{∣ - 3 ∣}{∣ 2 x - 1 ∣}

x^{2} - ∣ x + 2 ∣ + x > 0

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6