What is (|x|-5)(|x|-7)<= 0 ?

The solution to (|x|-5)(|x|-7)<= 0 is -7<= x<=-5\lor 5<= x<= 7

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(|x|-5)(|x|-7)<= 0

(∣ x ∣ - 5) (∣ x ∣ - 7) \leq 0

- 7 \leq x \leq - 5 or 5 \leq x \leq 7

Interval Notation

[- 7, - 5] \cup [5, 7]

Solution steps

(∣ x ∣ - 5) (∣ x ∣ - 7) \leq 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

- 7 \leq x \leq - 5 or 5 \leq x \leq 7

(c) ∣ x - 3 ∣ - ∣ x + 2 ∣ \leq 3

x^{2} + x + x - 1 < 0

∣ u - 6 ∣ < 5

\frac{1}{x} \geq ∣ x + 2 ∣

\frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )} > 1

What is (|x|-5)(|x|-7)<= 0 ?
The solution to (|x|-5)(|x|-7)<= 0 is -7<= x<=-5\lor 5<= x<= 7