What is |x^2-5x+4|-|x^2-4|<0 ?

The solution to |x^2-5x+4|-|x^2-4| 5/2

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|x^2-5x+4|-|x^2-4|<0

x^{2} - 5 x + 4 - x^{2} - 4 < 0

0 < x < \frac{8}{5} or x > \frac{5}{2}

Interval Notation

(0, \frac{8}{5}) \cup (\frac{5}{2}, \infty)

Decimal Notation

0 < x < 1.6 or x > 2.5

Solution steps

x^{2} - 5 x + 4 - x^{2} - 4 < 0

Find positive and negative intervals

x \leq - 2, - 2 < x \leq 1, 1 < x < 2, 2 \leq x < 4, x \geq 4

Solve the inequality for each interval

No Solution or 0 < x \leq 1 or 1 < x < \frac{8}{5} or \frac{5}{2} < x < 4 or x \geq 4

Merge Overlapping Intervals

0 < x < \frac{8}{5} or x > \frac{5}{2}

∣ x + 2 ∣ < 4 ∣ 2 x - 3 ∣

x^{2} - ∣ x + 2 ∣ + x => 0

∣ 4 - x ∣ < - 11

\frac{( x - 2 )}{( x - 2 )} \cdot (\frac{- 1}{2}) \leq 0

x^{2} - 4 \leq 0

What is |x^2-5x+4|-|x^2-4|<0 ?
The solution to |x^2-5x+4|-|x^2-4|<0 is 0<x< 8/5 \lor x> 5/2