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

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

∣ x + 3 ∣ + ∣ x - 1 ∣ < ∣ 6 - 3 x ∣

x < \frac{2}{3} or x > 8

Interval Notation

(- \infty, \frac{2}{3}) \cup (8, \infty)

Decimal Notation

x < 0.66666 \dots or x > 8

Solution steps

∣ x + 3 ∣ + ∣ x - 1 ∣ < ∣ 6 - 3 x ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < 1, 1 \leq x \leq 2, x > 2

Solve the inequality for each interval

x < - 3 or - 3 \leq x < \frac{2}{3} or No Solution or x > 8

Merge Overlapping Intervals

x < \frac{2}{3} or x > 8

\frac{x ^{2} - 1}{∣ x ^{2} + x + 1 ∣} < 1

x^{2} - 1 \leq 0

∣ 3^{x} - 5 ∣ < 1

x^{2} - 3 ∣ x ∣ - 10 < 0

∣ 3 t - 4 ∣ < 8

What is |x+3|+|x-1|<|6-3x| ?
The solution to |x+3|+|x-1|<|6-3x| is x< 2/3 \lor x>8