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

The solution to |x-1|+|x-3|<= 6 is -1<= x<= 5

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

∣ x - 1 ∣ + ∣ x - 3 ∣ \leq 6

- 1 \leq x \leq 5

Interval Notation

[- 1, 5]

Solution steps

∣ x - 1 ∣ + ∣ x - 3 ∣ \leq 6

Find positive and negative intervals

x < 1, 1 \leq x < 3, x \geq 3

Solve the inequality for each interval

- 1 \leq x < 1 or 1 \leq x < 3 or 3 \leq x \leq 5

Merge Overlapping Intervals

- 1 \leq x \leq 5

\frac{- 3}{x + \frac{1}{2}} < - 6

\frac{∣ x + 3 ∣ + x}{x + 2} > 1

∣ x - 3 ∣ > 2 x + 1

∣ 2 x - 4 ∣ < x - 1

x^{2} - x - 2 > 2