What is -10<(x+2)^2<20 ?

The solution to -10<(x+2)^2<20 is -2sqrt(5)-2<x<2sqrt(5)-2

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-10<(x+2)^2<20

- 10 < (x + 2)^{2} < 20

- 25 - 2 < x < 25 - 2

Interval Notation

(- 25 - 2, 25 - 2)

Decimal Notation

- 6.47213 \dots < x < 2.47213 \dots

Solution steps

- 10 < (x + 2)^{2} < 20

a < u < b

then

a < u and u < b

- 10 < (x + 2)^{2} and (x + 2)^{2} < 20

- 10 < (x + 2)^{2} :

True for all

x

(x + 2)^{2} < 20 : - 25 - 2 < x < 25 - 2

Combine the intervals

True for all x and - 25 - 2 < x < 25 - 2

Merge Overlapping Intervals

- 25 - 2 < x < 25 - 2

\frac{- 1}{5} < 3 \frac{x}{10} + 1 < \frac{2}{5}

2 \leq ∣ 2 x - 1 ∣ \leq 10

2 > 2 x > 10

x + 1 > 3 > 5 - 2 x

- 3 < - \frac{1}{2} - 2 \frac{x}{3} \leq \frac{5}{6}

What is -10<(x+2)^2<20 ?
The solution to -10<(x+2)^2<20 is -2sqrt(5)-2<x<2sqrt(5)-2