What is |x^2-6x+8|<= 4-x ?

The solution to |x^2-6x+8|<= 4-x is 1<= x<= 3\lor x=4

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|x^2-6x+8|<= 4-x

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

1 \leq x \leq 3 or x = 4

Interval Notation

[1, 3] \cup x = 4

Solution steps

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

Find positive and negative intervals

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

Solve the inequality for each interval

1 \leq x \leq 2 or 2 < x \leq 3 or x = 4

Merge Overlapping Intervals

1 \leq x \leq 3 or x = 4

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

∣ x - 1 ∣ + ∣ x + 2 ∣ \geq 3

\frac{1}{( 2 - ∣ x ∣ )} \geq 1

x^{2} - 3 x - 3 > x^{2} + 7 x - 13

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

What is |x^2-6x+8|<= 4-x ?
The solution to |x^2-6x+8|<= 4-x is 1<= x<= 3\lor x=4