What is |x|-|x-2|>= 1 ?

The solution to |x|-|x-2|>= 1 is x>= 3/2

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|x|-|x-2|>= 1

∣ x ∣ - ∣ x - 2 ∣ \geq 1

x \geq \frac{3}{2}

Interval Notation

[\frac{3}{2}, \infty)

Decimal Notation

x \geq 1.5

Solution steps

∣ x ∣ - ∣ x - 2 ∣ \geq 1

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or \frac{3}{2} \leq x < 2 or x \geq 2

Merge Overlapping Intervals

x \geq \frac{3}{2}

\frac{3 - x}{2} \leq 2

\frac{( 2 x - 4 )}{- 6} + 2 \leq 10

∣ z - 1 ∣ + ∣ z + 1 ∣ \leq 3

∣ 2 x + 3 ∣ > \frac{1}{2}

\frac{2 x - 3}{x - 1} > 3