x/x <3

Solution

\frac{x}{x} < 3

x < 0 or x > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

\frac{x}{x} < 3

Simplify

1 < 3

True for all x

Find singularity points

Find the zeros of the denominator

x : x = 0

Since the inequality is not defined for

x = 0

x < 0 or x > 0

Combine the intervals

True for all x and x < 0 or x > 0

Merge Overlapping Intervals

x < 0 or x > 0

(82)^{2}

\frac{∣ 2 + 3 x ∣}{2} \geq 5

4 x^{2} + 2 x - 9 = 0

\frac{4}{9}

x - 3 x^{2} \geq 0