What is |x-1|>= |x-3| ?

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

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|x-1|>= |x-3|

∣ x - 1 ∣ \geq ∣ x - 3 ∣

x \geq 2

Interval Notation

[2, \infty)

Solution steps

∣ x - 1 ∣ \geq ∣ x - 3 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or 2 \leq x < 3 or x \geq 3

Merge Overlapping Intervals

x \geq 2

(1 + x)^{2} \geq 1 - x^{2}

x^{2} - 6 x + 8 \leq 4 - x

x^{3} + 1 < x^{2} - x + 1

∣ x - 1 ∣ + ∣ x + 2 ∣ \geq 3

\frac{1}{( 2 - ∣ x ∣ )} \geq 1