What is |x^2-1|<0.5 ?

The solution to |x^2-1|<0.5 is -1.22474…<x<-0.70710…\lor 0.70710…<x<1.22474…

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|x^2-1|<0.5

x^{2} - 1 < 0.5

- 1.22474 \dots < x < - 0.70710 \dots or 0.70710 \dots < x < 1.22474 \dots

Interval Notation

(- 1.22474 \dots, - 0.70710 \dots) \cup (0.70710 \dots, 1.22474 \dots)

Solution steps

x^{2} - 1 < 0.5

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 0.5 < x^{2} - 1 < 0.5

x^{2} - 1 > - 0.5 and x^{2} - 1 < 0.5

(x < - 0.70710 \dots or x > 0.70710 \dots) and - 1.22474 \dots < x < 1.22474 \dots

Merge Overlapping Intervals

- 1.22474 \dots < x < - 0.70710 \dots or 0.70710 \dots < x < 1.22474 \dots

250 = 40 t - 0.8 t^{2}

3 x^{2} = 6 x

44

\frac{8}{6}

d (z - 2) + 5 (z - 2)

What is |x^2-1|<0.5 ?
The solution to |x^2-1|<0.5 is -1.22474…<x<-0.70710…\lor 0.70710…<x<1.22474…