What is |x^2-5x+4|>= 4-x ?

The solution to |x^2-5x+4|>= 4-x is x = 2

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|x^2-5x+4|>= 4-x

x^{2} - 5 x + 4 \geq 4 - x

x \leq 0 or x \geq 2

Solution steps

x^{2} - 5 x + 4 \geq 4 - x

Find positive and negative intervals

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

Solve the inequality for each interval

x \leq 0 or 2 \leq x < 4 or x \geq 4

Merge Overlapping Intervals

x \leq 0 or x \geq 2

x^{2} - ∣ 5 x + 8 ∣ > 0

\frac{- 1}{( ∣ x ∣ - 2 )} \geq 1

3 x^{2} - ∣ x - 3 ∣ > 9 x - 2

x^{2} - 2 x - 2 \geq x^{2} - 2

∣ x - 2 ∣ \leq 2 x^{2} - 9 x + 9