What is |x^2-3x-7|<3 ?

The solution to |x^2-3x-7|<3 is -2<x<-1\lor 4<x<5

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|x^2-3x-7|<3

x^{2} - 3 x - 7 < 3

- 2 < x < - 1 or 4 < x < 5

Interval Notation

(- 2, - 1) \cup (4, 5)

Solution steps

x^{2} - 3 x - 7 < 3

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 3 < x^{2} - 3 x - 7 < 3

x^{2} - 3 x - 7 > - 3 and x^{2} - 3 x - 7 < 3

(x < - 1 or x > 4) and - 2 < x < 5

Merge Overlapping Intervals

- 2 < x < - 1 or 4 < x < 5

3 \cdot 49

3 x + 1 - 2 x = 9 - 3

5^{0} \cdot 5^{3}

- \frac{5}{3} \cdot 3

ln (0.02)