What is |x-1|+|x-5|<= 10 ?

The solution to |x-1|+|x-5|<= 10 is -2<= x<= 8

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|x-1|+|x-5|<= 10

∣ x - 1 ∣ + ∣ x - 5 ∣ \leq 10

- 2 \leq x \leq 8

Solution steps

∣ x - 1 ∣ + ∣ x - 5 ∣ \leq 10

Find positive and negative intervals

x < 1, 1 \leq x < 5, x \geq 5

Solve the inequality for each interval

- 2 \leq x < 1 or 1 \leq x < 5 or 5 \leq x \leq 8

Merge Overlapping Intervals

- 2 \leq x \leq 8

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

∣ 2 (x - 1) + 4 ∣ < 4

∣ x - 1 ∣ + ∣ x - 3 ∣ \leq 6

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

\frac{∣ x + 3 ∣ + x}{x + 2} > 1