What is (((|x|-1)(|x|-2)))/((|x|-3))>= 0 ?

The solution to (((|x|-1)(|x|-2)))/((|x|-3))>= 0 is x 3

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(((|x|-1)(|x|-2)))/((|x|-3))>= 0

\frac{( ( ∣ x ∣ - 1 ) ( ∣ x ∣ - 2 ) )}{( ∣ x ∣ - 3 )} \geq 0

x < - 3 or - 2 \leq x \leq - 1 or 1 \leq x \leq 2 or x > 3

Interval Notation

(- \infty, - 3) \cup [- 2, - 1] \cup [1, 2] \cup (3, \infty)

Solution steps

\frac{( ∣ x ∣ - 1 ) ( ∣ x ∣ - 2 )}{∣ x ∣ - 3} \geq 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x < - 3 or - 2 \leq x \leq - 1 or 1 \leq x \leq 2 or x > 3

∣ 3 x + 5 ∣ > 17

- (\frac{1}{3}) ∣ 6 - 5 x ∣ + 2 \geq 1

∣ x ∣ + ∣ x - 1 ∣ < x + 4

3 x^{2} - 5 x > - 6

∣ 2 x + 1 ∣ > x

What is (((|x|-1)(|x|-2)))/((|x|-3))>= 0 ?
The solution to (((|x|-1)(|x|-2)))/((|x|-3))>= 0 is x<-3\lor-2<= x<=-1\lor 1<= x<= 2\lor x>3