What is x^2-5|x|+6>= 0 ?

The solution to x^2-5|x|+6>= 0 is x = 3

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x^2-5|x|+6>= 0

x^{2} - 5 ∣ x ∣ + 6 \geq 0

x \leq - 3 or - 2 \leq x \leq 2 or x \geq 3

Interval Notation

(- \infty, - 3] \cup [- 2, 2] \cup [3, \infty)

Solution steps

x^{2} - 5 ∣ x ∣ + 6 \geq 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

(x \leq - 3 or - 2 \leq x < 0) or (0 \leq x \leq 2 or x \geq 3)

Merge Overlapping Intervals

x \leq - 3 or - 2 \leq x \leq 2 or x \geq 3

x^{2} - 4 ∣ x ∣ + 3 < 0

∣ 4 (x - 1) + 10 ∣ \leq 22

∣ 3 x - 2 ∣ \geq ∣ x + 1 ∣

\frac{( x ^{2} - 5 x + 4 )}{( x ^{2} - 4 )} \leq 1

∣ x - 2 ∣ + ∣ x - 3 ∣ < 6

What is x^2-5|x|+6>= 0 ?
The solution to x^2-5|x|+6>= 0 is x<=-3\lor-2<= x<= 2\lor x>= 3