What is |x|-|x-1|+x>= 0 ?

The solution to |x|-|x-1|+x>= 0 is x>= 1/3

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|x|-|x-1|+x>= 0

∣ x ∣ - ∣ x - 1 ∣ + x \geq 0

x \geq \frac{1}{3}

Interval Notation

[\frac{1}{3}, \infty)

Decimal Notation

x \geq 0.33333 \dots

Solution steps

∣ x ∣ - ∣ x - 1 ∣ + x \geq 0

Find positive and negative intervals

x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

No Solution or \frac{1}{3} \leq x < 1 or x \geq 1

Merge Overlapping Intervals

x \geq \frac{1}{3}

- 12 x^{2} + 72 x

3 - \frac{4 x}{5} = \frac{4 + x}{5}

3 x + 5 \geq x + 2

2 k^{3} + 15 k^{2} + 25 k + 12

(x + 3)^{3} - (3 x - 1)^{2} = x^{3} + 4