5<x^2<50

The solution to 5<x^2<50 is -5sqrt(2)<x<-sqrt(5)\lor sqrt(5)<x<5sqrt(2)

Solution

5 < x^{2} < 50

- 52 < x < - 5 or 5 < x < 52

Interval Notation

(- 52, - 5) \cup (5, 52)

Decimal Notation

- 7.07106 \dots < x < - 2.23606 \dots or 2.23606 \dots < x < 7.07106 \dots

Solution steps

5 < x^{2} < 50

a < u < b

then

a < u and u < b

5 < x^{2} and x^{2} < 50

5 < x^{2} : x < - 5 or x > 5

x^{2} < 50 : - 52 < x < 52

Combine the intervals

(x < - 5 or x > 5) and - 52 < x < 52

Merge Overlapping Intervals

- 52 < x < - 5 or 5 < x < 52

0 < x < 1

5 < x < 10

(\frac{1}{5}) < (\frac{1}{y}) < (\frac{1}{3})

19 < 4 d - 1 < 47

4 x - 6 < 7 x - 12 < 3 x + 20

What is 5<x^2<50 ?
The solution to 5<x^2<50 is -5sqrt(2)<x<-sqrt(5)\lor sqrt(5)<x<5sqrt(2)