What is |x|+|x-2|<= 6 ?

The solution to |x|+|x-2|<= 6 is -2<= x<= 4

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|x|+|x-2|<= 6

∣ x ∣ + ∣ x - 2 ∣ \leq 6

- 2 \leq x \leq 4

Interval Notation

[- 2, 4]

Solution steps

∣ x ∣ + ∣ x - 2 ∣ \leq 6

Find positive and negative intervals

x < 0, 0 \leq x < 2, x \geq 2

Solve the inequality for each interval

- 2 \leq x < 0 or 0 \leq x < 2 or 2 \leq x \leq 4

Merge Overlapping Intervals

- 2 \leq x \leq 4

∣ x - 1 ∣ \leq 1

∣ 3 x ∣ > 5

x^{2} - ∣ x ∣ - 2 > 0

\frac{x + 1}{3} > \frac{8}{3}

x^{2} + x > x^{2} - 5 x - 8