What is |x^2-9|+|x^2-1|>8 ?

The solution to |x^2-9|+|x^2-1|>8 is x 3

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|x^2-9|+|x^2-1|>8

x^{2} - 9 + x^{2} - 1 > 8

x < - 3 or - 1 < x < 1 or x > 3

Interval Notation

(- \infty, - 3) \cup (- 1, 1) \cup (3, \infty)

Solution steps

x^{2} - 9 + x^{2} - 1 > 8

Find positive and negative intervals

x \leq - 3, - 3 < x \leq - 1, - 1 < x < 1, 1 \leq x < 3, x \geq 3

Solve the inequality for each interval

x < - 3 or No Solution or - 1 < x < 1 or x > 3

Merge Overlapping Intervals

x < - 3 or - 1 < x < 1 or x > 3

11 x - 9 < 3 x + 11 < 7 x + 13

- 3 < - 4 x + 1 < 13

1 \leq \frac{( 3 x ^{2} - 7 x + 8 )}{( x ^{2} + 1 )} \leq 2

2 < ∣ x ∣ \leq 5

- x < x^{2} < 6

What is |x^2-9|+|x^2-1|>8 ?
The solution to |x^2-9|+|x^2-1|>8 is x<-3\lor-1<x<1\lor x>3