What is |x^2-5x|>|x^2|-|5x| ?

The solution to |x^2-5x|>|x^2|-|5x| is x<0\lor 0<x<5

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|x^2-5x|>|x^2|-|5x|

x^{2} - 5 x > x^{2} - ∣ 5 x ∣

x < 0 or 0 < x < 5

Interval Notation

(- \infty, 0) \cup (0, 5)

Solution steps

x^{2} - 5 x > x^{2} - ∣ 5 x ∣

Find positive and negative intervals

x \leq 0, 0 < x < 5, x \geq 5

Solve the inequality for each interval

x < 0 or 0 < x < 5 or No Solution

Merge Overlapping Intervals

x < 0 or 0 < x < 5

∣ 2 x - 3 ∣ < ∣ x + 2 ∣

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

∣ 2 x - 1 ∣ + ∣ x ∣ \leq 10

x^{2} - 3 x + x - 2 < 0

∣ x - 3 ∣ - ∣ x - 3 ∣ - ∣ x + 4 ∣ \leq 10

What is |x^2-5x|>|x^2|-|5x| ?
The solution to |x^2-5x|>|x^2|-|5x| is x<0\lor 0<x<5