What is |x^2-9|<0.1 ?

The solution to |x^2-9|<0.1 is -3.01662…<x<-2.98328…\lor 2.98328…<x<3.01662…

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|x^2-9|<0.1

x^{2} - 9 < 0.1

- 3.01662 \dots < x < - 2.98328 \dots or 2.98328 \dots < x < 3.01662 \dots

Interval Notation

(- 3.01662 \dots, - 2.98328 \dots) \cup (2.98328 \dots, 3.01662 \dots)

Solution steps

x^{2} - 9 < 0.1

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 0.1 < x^{2} - 9 < 0.1

x^{2} - 9 > - 0.1 and x^{2} - 9 < 0.1

(x < - 2.98328 \dots or x > 2.98328 \dots) and - 3.01662 \dots < x < 3.01662 \dots

Merge Overlapping Intervals

- 3.01662 \dots < x < - 2.98328 \dots or 2.98328 \dots < x < 3.01662 \dots

\frac{200 x ^{3} y}{2 x y ^{5}}

16 s^{4} + 36 s^{3} b - 10 s^{2} b^{2}

y^{- 4}

18 = 6 x + x (x - 13)

x^{2} - 10 x + 19 = 0

What is |x^2-9|<0.1 ?
The solution to |x^2-9|<0.1 is -3.01662…<x<-2.98328…\lor 2.98328…<x<3.01662…