-3< 1/x <1

Solution

- 3 < \frac{1}{x} < 1

x < - \frac{1}{3} or x > 1

Interval Notation

(- \infty, - \frac{1}{3}) \cup (1, \infty)

Decimal Notation

x < - 0.33333 \dots or x > 1

Solution steps

- 3 < \frac{1}{x} < 1

a < u < b

then

a < u and u < b

- 3 < \frac{1}{x} and \frac{1}{x} < 1

- 3 < \frac{1}{x} : x < - \frac{1}{3} or x > 0

\frac{1}{x} < 1 : x < 0 or x > 1

Combine the intervals

(x < - \frac{1}{3} or x > 0) and (x < 0 or x > 1)

Merge Overlapping Intervals

x < - \frac{1}{3} or x > 1

\frac{0}{15}

5 x^{2} - 4 x + 3 = 0

(3 g^{4} + 5 g^{2} h + 1) - (3 g^{4} - 5 g^{2} + 8 h)

\frac{( x - 1 ) ( x + 2 )}{( x - 3 )} \geq 0

c^{3} + 8 d^{3}