What is 7<2(x^2)+1<= 19 ?

The solution to 7<2(x^2)+1<= 19 is -3<= x<-sqrt(3)\lor sqrt(3)<x<= 3

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7<2(x^2)+1<= 19

7 < 2 (x^{2}) + 1 \leq 19

- 3 \leq x < - 3 or 3 < x \leq 3

Interval Notation

[- 3, - 3) \cup (3, 3]

Decimal Notation

- 3 \leq x < - 1.73205 \dots or 1.73205 \dots < x \leq 3

Solution steps

7 < 2 (x^{2}) + 1 \leq 19

a < u \leq b

then

a < u and u \leq b

7 < 2 (x^{2}) + 1 and 2 (x^{2}) + 1 \leq 19

7 < 2 x^{2} + 1 : x < - 3 or x > 3

2 x^{2} + 1 \leq 19 : - 3 \leq x \leq 3

Combine the intervals

(x < - 3 or x > 3) and - 3 \leq x \leq 3

Merge Overlapping Intervals

- 3 \leq x < - 3 or 3 < x \leq 3

2 x - 3 < x + 1 \leq 4 x + 7

- 8 < 5 x - 3 < 7

x - 3 < 2 (x - \frac{1}{2}) \leq x + 4

n - 4 < 3 n < 4 n + 4

5 < x^{2} < 50

What is 7<2(x^2)+1<= 19 ?
The solution to 7<2(x^2)+1<= 19 is -3<= x<-sqrt(3)\lor sqrt(3)<x<= 3