What is |x^2-81|<0.45 ?

The solution to |x^2-81|<0.45 is -9.02496…<x<-8.97496…\lor 8.97496…<x<9.02496…

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|x^2-81|<0.45

x^{2} - 81 < 0.45

- 9.02496 \dots < x < - 8.97496 \dots or 8.97496 \dots < x < 9.02496 \dots

Interval Notation

(- 9.02496 \dots, - 8.97496 \dots) \cup (8.97496 \dots, 9.02496 \dots)

Solution steps

x^{2} - 81 < 0.45

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 0.45 < x^{2} - 81 < 0.45

x^{2} - 81 > - 0.45 and x^{2} - 81 < 0.45

(x < - 8.97496 \dots or x > 8.97496 \dots) and - 9.02496 \dots < x < 9.02496 \dots

Merge Overlapping Intervals

- 9.02496 \dots < x < - 8.97496 \dots or 8.97496 \dots < x < 9.02496 \dots

\frac{1}{3} (\frac{2}{3})

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

36 < 6 j

\frac{8 + 7 i}{3 - 4 i}

y + 8 = 0

What is |x^2-81|<0.45 ?
The solution to |x^2-81|<0.45 is -9.02496…<x<-8.97496…\lor 8.97496…<x<9.02496…